BBC verse, John/Sherlock. John's last (only?) boyfriend was horrible and treated him badly, borderline domestic abuse, so he's not exactly enthusiastic about entering into a relationship with Sherlock because he thinks it'll be the same. I think the ex's name was Tom? Sherlock never finds out who he is (although of course he wants to, so he can exact revenge) and he sets about convincing John that it can be better. And it is.
The story is a classic and awesome and deliciously slow paced and gentle. I think I read it on AO3 before. Any clues are appreciated, thanks!
EDIT: Found! Thank you to
homeflight for finding
A Live Well Lived by
kate_lear.