Place the rabbit pieces in a large bowl and toss with the sprigs of rosemary, thyme, and sage, 2 cloves of the garlic, and 3 tablespoons (45 ml) of the oil. Set aside to marinate for 4 hours.
In a large sauté pan, heat ½ tablespoon of the remaining oil, add the rabbit pieces and sauté over high heat until they are lightly browned. Remove them from the pan.
Add the carrot, celery, onion, and remaining garlic to the pan, sauté until the vegetables are tender. Add the tomatoes to the pan, then stir in the wine.
Bring to a simmer, return the rabbit pieces to the pan, and season with salt and pepper.
Add a little water if necessary, so that the rabbit is barely covered with the sauce. Preheat the oven to 350°F (180°C).
Place a piece of foil directly on the surface of the ingredients, place the pan in the oven, and bake for 2 hours.
Add a little more water if necessary. While the rabbit is baking sauté the mushrooms over high heat in the remaining ½ tablespoon of oil.
After the rabbit has baked for 1 ½ hours, add the sauté mushrooms to the pan.
When the rabbit is done, check the seasonings. Add the chopped herbs and serve.