My Grandfather used to cook rabbit in a similar way with a brown onion gravy. It was wonderful! His mother, my Great Grandmother raised rabbits for food. I have no idea the breed maybe wild? I remember she had a long row of pens for them. Granddaddy also cooked squirrel the same way. You never knew what he was cooking. lolWe've had good luck in the past baking in earthenware with root veggies, mushrooms, and then finishing with a sour cream sauce - and yes, I think it was a shallow braise, but I'd have to look the recipe up again.
Lovely memories. I miss them both. They could do anything!