RIGHT? I'm having real trouble! There's the vet-themed fantasy series I mentioned in a comment above (The Magic and the Healing is the first one -- it's about a bunch of vet students who go on rotational rounds to a magical fantasy land) but given that the heroine has a terminal disease and there's a lot of murder and emphasis on the fact that veterinary medicine can be tough and depressing I remember it as kind of too dark to be called cozy. I think there's also an fantasy series about a werewolf who hosts a radio talk show, but I haven't read it -- that's the one I was thinking of when I said urban fantasy got there first, though, because the cover definitely seem super urban fantasy even though the conceit could conceivably be cozy-theme-style. Maybe Mercedes Lackey's racecar elves series? But given the focus on ABUSED CHILDREN!!! in those books, I wouldn't exactly call that cozy either...

I don't know, if anyone else has thoughts, please chime in!