Snap the leaves off the artichokes until only the tender inner leaves remain. Snap off the stem. Trim the remaining green bits from the bottom of the artichoke, and cut off the inner leaves in a bunch at the point where they are very tender. Pare the tough green outer layer off the remaining stem, pairing the stem into a point. Now cut the artichoke bottom into quarters and remove the choke with a sharp knife from each quarter. Rinse to remove any traces of foin ("hay") and drop them into a bowl of water acidulated with the juice of half a lemon.
Heat 2 T olive oil in a large heavy casserole or Dutch oven. Dredge the rabbit pieces in seasoned flour, shaking off excess. Brown over medium heat, turning regularly, until golden on all sides. Remove rabbit pieces to a plate and dump any oil remaining in the pan. Add 1 T of the remaining oil and the bacon dice. (Omit bacon if you only have access to the thin-sliced vacuum packed supermarket variety.) SautÚ until cooked but not "crisp". Add the remaining T of oil and the onion and carrot. Saute for 5 minutes, then add the artichoke quarters and the garlic, stir one minute, and add the tomatoes and the white wine. Turn up the heat and reduce until syrupy, stirring constantly, for about 5 minutes. Lay the bouquet garni on top of the vegetables. Arrange the rabbit pieces on top, together with any juice accumulated in the plate.
Pour in enough broth to come halfway up the sides of the rabbit pieces. Cover and bring to a simmer. Continue to simmer over very low heat about 1 hour or cook in the oven at 350 degrees for the same amount of time. The rabbit should be just tender and part readily from the bone. Don't overcook or it will become dry. Check the liquid level frequently and add more broth if necessary. Turn the rabbit pieces once.
When done, remove the rabbit pieces to a warm platter and arrange the vegetables, removed with a slotted spoon, around them. Cover and keep warm. Strain the remaining pan juices into a smaller saucepan and reduce over high heat, skimming frequently, until reduced by 1/3. Pour over the platter and serve immediately. Sprinkle with finely chopped flat-leaf parsley if you like.