Prepare the rabbit: After butchering cleaning and resting your rabbit, cut it into serving pieces (typically legs, loins, and shoulders). Pat the pieces dry with paper towels.
Season and dredge: Place the flour in a shallow dish and season with salt and pepper. Coat each piece of rabbit with the seasoned flour, shaking off excess.
Brown the meat: Heat oil in a large Dutch oven over medium-high heat. Brown the rabbit pieces on all sides, working in batches if necessary to avoid overcrowding. Transfer the browned meat to a plate.
Build the flavor base: In the same pot, add the onions and carrots. Cook until softened, about 5-7 minutes. Add the garlic and cook until fragrant, about 1 minute more.
Deglaze and simmer: Return the rabbit to the pot. Add thyme, bay leaves, and tomato paste, stirring to coat. Pour in the wine if using, scraping up any browned bits from the bottom of the pot. Add the stock and bring to a simmer.
Slow cook: Reduce heat to low, cover, and simmer gently for about 1 hour, or until the rabbit is becoming tender.
Serve: Remove bay leaves. Garnish with fresh parsley and serve with crusty bread to soak up the delicious gravy.