A character — frequently male — who is only able to make one specific kind of food, often because they're a Lethal Chef and attempts to diversify their efforts would end in disaster. Through harsh training, they have finally become able to make one thing that is edible, at least. If it's their Trademark Favorite Food, they're in luck. Sometimes their specialty dish is widely praised as being transcendentally delicious... they just can't transfer that skill to anything else.
Sometimes Truth in Television — it's relatively common for people who aren't particularly good at cooking (even if they're not quite at Lethal Chef levels) to be able to make a few dishes fairly well. This trope lies somewhere between Supreme Chef and Lethal Chef.
Nerine of SHUFFLE! can't cook, but after taking cooking lessons, she is able to make omelets (and only omelets) for lunch, in large quantities. Before she took lessons, her cooking attempts usually resulted in explosions and something worse, so when she finally learned how to cook omelets her dad wanted to create a holiday to celebrate.
Akane Tendo of Ranma ½ is a Lethal Chef, but it's said that when she really tries her curry is bearable, "Maybe... even tasty."
Ukyou, who is otherwise considered a Supreme Chef, rarely bothers cooking anything that isn't okonomiyaki. To the point that when she tried to give it up, she suffered withdrawal symptoms and ended up cooking Ranma like an okonomiyaki.
One episode of Sailor Moon has Usagi trying to cook and failing badly... until she makes curry, which Mamoru and Chibi-Usa both enjoy, the latter even asking "Can we have this every night?" In the rest of the series she's a Lethal Chef - especially when it comes to curry.
Rei herself isn't much of a cook either unless it's food that comes prepackaged like curry. In one episode when the girls went on a picnic, Rei teases Usagi's shoddy attempt at home cooking leading to Usagi pointing out that at least she tried while Rei just bought fast food. In a later episode during Rei's little Imagine Spot of the things she can cook, like instant curry, she's shoved all the packages inside a food processor without even opening them.
Ringo Oginome of Mawaru-Penguindrum starts the series only being able to make curry, but learns how to cook more things under Himari, Shouma and Kanba's tutelage. It also serves a metaphor for her Character Development, since curry represents her clinging to her past, and specifically the memory of her dead older sister Momoka, who loved curry to death.
Despite the characters from Anpanman that are themed around prepared foods and meals being the best at whatever they cook, this is the ONLY thing they cook. Compared to characters with a single ingredient theme (like a single vegetable or fruit), this leads to a lot of episodes based on two of these characters battling over whose dish is the best. This is also the driving point of practically every argument the Donburiman Trio has gotten into: which donburi dish is the tastiest.
While she starts out as a Lethal Chef, Yui in K-On! once had to take the reins of house-duty when her sister Ui was sick. While Yui couldn't do all that much on her own, she did teach herself to make a mean okayu to help Ui get better. She later used this same knowledge to help Sawako, who was also sick.
Umi Ryuzaki from Magic Knight Rayearth claims that she is excellent at baking, "but terrible at anything else"
Calvin's Dad: Since your mom's sick, I'm making dinner tonight. Calvin:You can cook? Calvin's Dad: As you can see, I survived two years of my own cooking when I had an apartment after college. Calvin: Mom says you ate frozen waffles and canned soup three times a day. Calvin's Dad: Your mom wasn't there, so she wouldn't know. Get the syrup out, will you?
Green Arrow is legendary amongst the hero community in The DCU for his chilli recipe. There is zero indication that he knows how to cook anything else.
Notably, his chilli isn't necessarily regarded as good, just really, really hot.
The only thing Empowered can cook is blueberry pancakes, although her friends note that they may not be the greatest, they eat them with gusto to cheer Emp up whenever she does cook.
Catman only ever cooks eggs, though he once claimed he could "also make a mean slab of raw zebra haunch."
The remake of The Parent Trap has the father offer to make dinner for his ex-wife. She's surprised that he's learned to cook. It turns out he can make "pasta... or pasta... or pasta." She plays along and says "the pasta sounds good."
The older brother in Zathura can make one thing: water.
Albert, The Grim Reaper's manservant in Discworld novels, can only make fry-ups. He will experiment with porridge or Hogswatch pudding, but only by frying them. Fortunately, Death doesn't need to eat.
It should be noted that it's not that Albert can't make anything un-fried, it's that he can't wrap his brain around un-fried food, since that's all he ever eats. The fried porridge thing was considered progress.
If porridge is a mixture of oatmeal, milk and water then by adding yeast, letting it work for an hour and then frying it you get Staffordshire Oatcakes, which are more than respectable food.
He did manage a mug of cocoa once. Well, he was close. If you turned the mug sideways, it would pour out eventually.
Lady Sybil Vimes can similarly only do a fry-up, and that's usually frazzled. Fortunately, years as a street copper have resulted in Sam Vimes actually preferring greasy, frazzled food.
Aimsbury in Making Money can actually cook a few things, but they're all fit for a dog to eat (Topsy Lavish, an eccentric old lady, hired him to cook for her Mister Muffykins) and therefore made of odd meats that most humans would rather avoid. He even asks "Have you seen my book, Cooking with Brains?" He prefers cooking for a dog because he has to stay out of professional kitchens due to an allergy to the word "garlic".
Something of a reversal, rather than only making one dish, the cook in Alice in Wonderland seems to think the only ingredient is pepper. It isn't elaborated whether or not she is actually able to make anything out of this or not, but given that it's Alice in Wonderland it is definitely possible.
Most of Miss Mush's food in the Wayside series causes extremely bizarre side effects, so the students avoid it. The exception is milk and nothing. Some students even got seconds of nothing, but then Miss Mush ran out of nothing.
In How I Met Your Mother, Lily tells Marshall how delicious his pancakes are and ask if he would like to make dinner sometime. He responds "Sure... how about pancakes?"
In the sitcom Alice, Mel's cooking is routinely slammed - even by his regular customers (curious for a diner that's apparently been running for years). Yet, he apparently makes a mean chili. (It sneaks in as a plot point in several episodes.)
Lois and Clark: "I can only make 4 things, and this is the only one without chocolate..."
Charlie from Two and a Half Men tries to learn to cook. He asks everyone how they want their eggs, and no matter what the answer is, he responds "Scrambled it is."
Debra from Everybody Loves Raymond can only cook lemon chicken. Everything else is disgusting. There was an episode titled "Debra Makes Something Good" where she makes braciole. However, she stops making it after that episode.
Subverted with Luke on Gilmore Girls - supposedly only cooks diner food, but turns out to be into fusion cuisine and high-end italian cooking.
When he travels back in time, the grown Hiro Nakamura is mistaken by his father to be the new chef (the Hiro of that time was a young boy). His mother orders eggs... but all Hiro knows how to make is waffles. She isn't mad at him.
Mistress Ploppy in Blackadder II, who prepares whatever the condemned prisoners want for their final meal. As long as they want sausages.
On Sweet Genius, preparing the same kind of dessert for two rounds will earn chefs a tongue-lashing from the judge. This came up frequently in the first season where the Baked round was followed by the Chocolate round, and chefs tended to make chocolate cakes for both. To be a Sweet Genius, one must be versatile.
Somewhat of an example with Lethal Chef Raine in Tales of Symphonia, gameplay-mechanics-wise. Her cooking skill for almost all of the recipes in the game max out at two stars (for most characters, that only applies to a few recipes they happen to be "bad" at). However, her ability to cook spaghetti is better than that for the other recipes... that one maxes out at three stars. (And she starts out with one star on that recipe, instead of starting with zero stars for all the other recipes.)
In the same game, Colette will add fruit to a good amount of her recipes (and the recipes she's best at are fruit-based). This is taken to the extreme in a skit in the sequel.
Flora of the Harvest Moon series is a Lethal Chef for anything that isn't curry. She knows it, hence it's all she cooks. Unfortunately for her, this has resulted in her boss/love interest Carter being sick to death of the stuff.
Otacon's adopted daughter, Sunny, is incapable of cooking anything but eggs. Justified in that she also lives in an airplane and presumably subsists entirely on military styled rations and eggs from the three chickens on the plane. At one point, she attempts to cook a block of ramen in the same manner as fried eggs (by plopping it in a frying pan), and ends up setting a fire.
Ms. Dungeon from Legasista is capable of making a variety of foodstuffs. The only problem is that the only ingredients to be found in the Ivy Tower are bean sprouts (both sentient and non-sentient), meaning that everything she makes tastes like bean sprouts, much to Alto's disgust.
In The Sims 2, sims who botch using the ReNuYu Aspiration Changer end up with the "Grilled Cheese" aspiration. All their wants, fears, and dreams revolve around cooking, eating, and serving grilled cheese sandwiches. In addition, grilled cheese sandwiches normally require two skill points in Cooking and can only be cooked for lunch or dinner, but Grilled Cheese sims can prepare them at any time, without any points in Cooking.
In Lightning Returns: Final Fantasy XIII when a chef asks Lightning for help in preparing one of his recipes, she admits she's only good at grilling Behemoth steak over a campfire. Fortunately for her, it turns out the chef only needs her help to gather ingredients and not actually cook.
Everyone who cooks in Mordavia in Quest for Glory IV has some kind of compulsion to put garlic in everything. Lots and lots of garlic. It might have something to do with the vampires running around, or that the creature that acts as the Dark One's symbol likes garlic.
Brewster from the Animal Crossing knows how to make really good coffee...and nothing else.
Tohno Shiki from Tsukihime is good at making noodles.
Inverted in Kanon where Akiko can make everything, except a Special Jam which can file her under Lethal Chef.
Haruka from Little Busters! can make some quite nice egg dishes if she works hard on them, but is pretty terrible at anything else. This is because her twin sister Kanata told her that she was allergic to eggs when they were little, so Haruka focused on them as the one thing she could do that Kanata couldn't.
When it's Rin's turn to cook in Fate/stay night, she's careful to stick with the few dishes she's confident at making.
In Mickey Tries To Cook, Minnie berates Mickey for only being able to make Cheese Ham and Tomato sandwiches, and thus that's all they ever eat at picnics. Mickey's attempts to learn how to cook something else ends in disaster.
Arguably SpongeBob SquarePants. When he trades places with a chef for a fancy restaurant, his attempts at haute cuisine end up turning into Krabby Patties.
An early episode showed him as having no idea what a sa-lad was. When he learned, the concept of tomatoes and lettuce without a bun and patty freaked him out.
In an episode of The Venture Bros., Sergeant Hatred takes over Hank's greasy spoon diner he's opened on the family compound, but admits that he only knows how to make scrambled eggs with ketchup.
Doug, and maybe by extension his entire family, has several books on making grill cheese sandwiches. That suggests Doug can make mean cheese sandwiches.
Courage the Cowardly Dog: After Muriel's Aunt Gertrude confides that vinegar is the secret ingredient to her famous raspberry jam, she begins putting it in every dish she makes thereafter (candy, pancakes, PB&J sandwiches, etcetera, etcetera). Her resultsvary.
Ed, Edd n Eddy: Eddy often brags at others (especially when he's cooking) on how his omelets are the best and everyone needs to try them. For everything else, he's a mess at the kitchen, if the cooking class at school is any evidence.
Bob Belcher from Bob's Burgers makes good burgers - Fantasticburgers, when it really matters. And of course, him being a One-Note Cook is justified by the fact that his restaurant is named...well, Bob's Burgers.
Although not that common in the U.S., many countries with a strong culture of cheap outside dining will have cooks who are extremely good at making things like tacos, pancakes, noodles, etc. These same cooks may also be absolute shit at cooking anything else, sometimes not even being able to cook their own meals aside from their specialty.
Chef Duff from Ace Of Cakes subverted this when he performed on Iron Chef America, and made excellent food. He still lost to Michael Symon, though.
Bobby Flay gets accusations of this. While he's usually not abysmal at cooking outside of his element, his style heavily leans on usage of hot peppers - you can practically predict how close of a match he'll have in Iron Chef or Throwdown based on how well the secret ingredient/proposed dish would work with spicy peppers thrown in.
Since professional cooking encompasses such a wide variety, it is inevitable that there are certain cooks/chefs who are specialists. As such, while they may be excellent, even famed, at said specialization, they might not do so well outside of it.