"Miles Gloriosus" is Latin for "boastful soldier", and even before Plautus the term was used for a comic stock character in Roman theater.
As usual with Plautus, there is some influence from an older Greek stock character: "alazon" (αλαζών) which means braggart and/or arrogant, depending on the context. "The alazôn is an impostor that sees himself as greater than he actually is." He might be a soldier, a scholar, an artist, etc. He is typically coupled with a sarcastic character whose comments undermine the seriousness of any given argument. A particularly memorable example exists in "The Acharnians" (425 BC) by Aristophanes. Lamachus , a historical general, is presented as a "rabid militarist" who makes a speech as to the reasons the ongoing war should be prolonged. Dikaiopolis (the protagonist) mocks the rather pompous arguments and attire of his opponent. Reducing Lamachus to a laughing stock. That Lamachus was using empty threats of violence but fails to react to even the greatest insults, probably points to the brave general being just another blowhard.
Falstaff comes close, though his protestations of bravery tend to be so absurd that even he probably doesn't take them seriously.
Rodrigo of Othello fits the "God's gift to women" version of this, paying a character who seems to fit the traditional clever servant role to help him in his quest to seduce Desdemona. Unfortunately, that other character happens to be Iago, and rather than the Humiliation Conga these characters often get, Rodrigo ends up as one of several corpses in the play.
Dick Dauntless in Ruddigore. His entrance song is about how his sloop turned tail and fled from a formidable French frigate, which of course they could have taken on... but... um... decided not to, just now. Because fighting them would be mean. Yeah, that's it.
Played with in The Pirates of Penzance. The "modern Major-General" Stanley claims to know pretty much everything and is extremely, gloriously proud of it... but he finally mentions at the end of his song that he happens to be inept at his actual job. Result: the related trope (named after him, naturally), Modern Major General!
Subverted by the Duke of Plaza-Toro in The Gondoliers - he sings a song boasting (quite truthfully) about his cowardice.
Lewis in Pippin, a strong stupid type who likes wearing shiny breastplates, swinging a sword around and boasting about the number of enemies slain by his hand.
Cyrano de Bergerac: At Act II Scene III, The Muskeeter is identified as this by Raguenau, who doesn't seem to realize (or care) that he is his wife's lover.