A lot of people recommend those epic-scale AU crossovers, but I honestly think the best character-driven stuff happens on a much smaller scale. I spent a whole weekend bingeing fics centered on Adolin in the immediate aftermath of the Sadeas thing. The ones that just have him talking to Renarin, or trying to have a painfully awkward dinner with Dalinar, where the entire conflict is just the weight of what he did sitting in the room with them—that's the good stuff. There's this one, 'Shards of a Mirror' on AO3, that's literally just Adolin and Kaladin stuck on a long carriage ride together after a diplomatic mission goes wrong. No fighting, no Voidbringers, just two guys who fundamentally misunderstand each other having to navigate a conversation for six hours. The author nails the way Kaladin's silences are just as loud as his speeches, and Adolin's internal monologue is a perfect blend of well-meaning privilege and genuine emotional confusion.
If you want real drama, skip the romance-centric tags for a bit and look for fics tagged 'Dalinar Kholin & Gavilar Kholin' or 'Evi Kholin'. The exploration of that family's trauma, pre-'Oathbringer' memories, is brutal and beautifully done. I read one from young Renarin's perspective, watching his father's 'episodes', that made me put my phone down and stare at the wall for a good ten minutes. The drama isn't in shouted arguments; it's in the quiet, horrific realization a child has that the strongest man he knows is broken. Those fics often have fewer kudos because they're not about popular ships, but the character work is consistently some of the most insightful I've seen in the fandom. They get into the gritty, unglamorous mechanics of living with guilt and inherited pain, which is basically the core theme of the books anyway.