If not already jointed, pat the rabbit dry and using a sharp chef’s knife or cleaver, cut between the joints to separate the front legs, hind legs, and saddle (back). Leave bones attached to keep pieces whole. Season pieces lightly with 1 tsp coarse salt and 1 tsp black pepper.

In a large bowl or resealable bag combine 1 cup dry white wine or cider, 3 tbs olive oil, smashed garlic cloves, 2 sprigs rosemary, 4 sprigs thyme, 2 bay leaves and the seasoned rabbit pieces. Turn to coat, cover or seal and marinate in the refrigerator for 2–4 hours (or up to overnight) to develop flavor. Remove rabbit from marinade and reserve the marinade and aromatics for later.

Braising Base

Prepare aromatics

Remove rabbit pieces from the marinade and pat very dry with paper towels (drying helps with browning). Strain the marinade into a bowl and discard solids (or reserve garlic and herbs if you want to add back later).

Brown the rabbit

In a large heavy-bottomed Dutch oven or wide ovenproof skillet, heat 2 tbs olive oil and 2 tbs unsalted butter over medium-high heat until shimmering. Working in batches to avoid crowding, add rabbit pieces skin-side down (or meaty side) and brown until deep golden (about 4–5 minutes per side). Transfer browned pieces to a plate and set aside.

Sauté vegetables

Reduce heat to medium. Add the sliced onion, carrots and celery to the pot and cook, stirring occasionally, until softened and beginning to color, about 6–8 minutes. Add the mushrooms and cook 3–4 more minutes until they release liquid and begin to brown.

Build the sauce

Stir in 1 tbs tomato paste and cook 1 minute. Sprinkle 2 tbs flour over the vegetables and stir for 1 minute to remove raw flour taste. Pour in 1 cup dry white wine (the reserved marinade can be added here if desired — use up to 1/2 cup reserved marinade and reduce the wine accordingly) to deglaze, scraping up browned bits from the bottom with a wooden spoon. Let the wine reduce by about half, 2–3 minutes.

Braise

Return the rabbit pieces to the pot, nestling them among the vegetables. Add 2 cups chicken or vegetable stock, 1 bay leaf, 2 thyme sprigs, 1 rosemary sprig and 1 tsp salt. If using, stir in 1 tsp mustard. Bring to a gentle simmer, then cover and transfer to a preheated oven at 325°F (160°C). Braise until meat is very tender and nearly falling from the bone, about 1 to 1 1/4 hours. Alternatively, simmer gently on the stovetop, partially covered, for the same time.

Check for doneness

Remove the pot from the oven. Carefully lift a piece of rabbit; it should feel tender and the meat should pull easily from the bone. If not ready, return to the oven and check every 10–15 minutes.

Finishing and Garnish

Mount and reduce sauce

Transfer rabbit pieces to a warm platter and tent with foil. Remove and discard the bay leaf and herb stems. Place the Dutch oven over medium-high heat and simmer the braising liquid until it reduces slightly and thickens, about 5–8 minutes. If you prefer a smoother sauce, spoon the solids into a blender or use an immersion blender and purée to desired consistency, then return to the pot.

Off the heat, whisk in 1 tbs cold cubed butter to enrich and slightly thicken the sauce. Taste and adjust seasoning with salt and pepper.

Serve

Arrange rabbit pieces on a platter or individual plates, spoon the sauce and vegetables over the top, and sprinkle with 2 tbs chopped fresh parsley and optional 1 tsp lemon zest for brightness. Serve with mashed potatoes, polenta, or crusty bread to soak up the sauce.