As a Moments page, all spoilers will be unmarked! Proceed with caution.
Pretty much any Friendship Moment between Morrigan and Hawthorne... but especially the moment when she, after a scary story she told got out of hand, ends up telling him her entire backstory, including being a cursed child, chased by the Hunt of Smoke and Shadow, and being an illegal immigrant. Hawthorne's reaction is golden:
Hawthorne stayed quiet until she'd finished, and for a little while afterwards. He looked dazed. Morrigan watched him, biting her lip, worried she'd said too much. Perhaps she should have left out the bit about coming from the Republic and being in Nevermoor illegally. And the bit about the curse. And all the other bits. "No offence," he said finally, "but that story's way better than the one you made up." The air left Morrigan's lungs in a low whoosh. It was typical of Hawthorne to take the strangeness of her life in stride, but she was deeply relieved nonetheless. "Hawthorne, you have to keep it a secret," Morrigan said. "I wasn't supposed to tell. If anybody finds out — if Inspector Flintlock —" Hawthorne held out his little finger. "Morrigan Crow," he said solemnly. "I pinkie promise to keep your secret and not tell another soul." Morrigan raised an eyebrow. "You pinkie what?" "Pinkie promise." He pushed his little finger closer to her face. "I've never broken a pinke promise in my life. Never." She hooked her pinkie in his, and they nodded. "Now," he said, frowning. "Please tell me that bit about getting chased through the clock by hunters with guns while driving a giant spider again."
When Inspector Flintlock first visits the Hotel Deucalion in order to accuse Morrigan of being an illegal immigrant, and uses some pretty nasty language, every single person present, from Fenestra to Frank, stands up for her. Though Jupiter is the one who manages to send Flintlock away with the revelation that Morrigan can't be legally prosecuted for anything as long as she's participating in the Trials, just the moment where everyone's ready to defend her is a huge moment. In the Republic, Morrigan was unwanted and feared by society in General; but at the Deucalion, though she hasn't lived there for very long, everyone's already protective of her.
Morrigan confides in Jupiter that she doesn't think she actually has a knack, or worse, that her perpetual bad luckis her knack. Jupiter immediately shuts that down.
Jupiter: You asked me if your talent is being cursed? If you have a knack for ruining things? Hear me when I tell you this: you are not a curse on anyone, Morrigan Crow.
In the second book, one Wundersmith's so-called act of cruelty is revealed to be an act of pure kindness. That huge theme park he built that no one could get into into? Turns out, some people can get in. He built it specifically for children who lived in the poorest area of Nevermoor, who would otherwise likely never get to go to a theme park. He enchanted it so it bars entrance to everyone else, but any child under the age of thirteen who's a resident of the neighborhood can get in any time for free, so they can have a place where they could have a fun, truly magical experience just for themselves. When Morrigan and Jupiter stand outside the gates, they can hear the laughter of the kids inside, having a great time.
It was the happiest Morrigan had ever felt to be excluded.
How righteously angry Jupiter gets on Morrigan's behalf when he finds out how she was treated for the first eleven years of her life. He may never lose his temper or go into detail about his anger in front of her, but it's obvious he's utterly furious at Corvus, Ivy, and every other person who treated her like she was a burden simply for existing. After seeing Morrigan be mistreated in the first few chapters of the first book, Jupiter's treatment of her is a breath of fresh air.