Divide the rabbit into 6-8 portion pieces, wash and pat dry. Peel onion and garlic and dice finely. Clean and wash the celery and also cut into fine cubes. Carve tomatoes crosswise, put them in boiling water for about 1 minute and rinse with cold water.
Skin the tomatoes and dice them roughly. Wash parsley, rosemary and thyme and shake dry. Chop the parsley, pluck the thyme leaves from the stalks. Heat 4-5 tablespoons of olive oil in a large frying pan.
Brown the rabbit parts all around. Add onions, garlic, celery and parsley and fry briefly. Season rabbit with salt and pepper, sprinkle with thyme and deglaze with white wine.
Add tomatoes, olives and rosemary twigs, bring to the boil, cover and stew for about 1 1/2 hours. Remove the sensitive back pieces after 15-20 minutes so that they do not become too dry. At the end of the braising time, place the back pieces in the roasting pan again and braise for about 5 minutes.
(Possibly braise for 10 minutes without lid at the end of the cooking time if the braising stock is still too thin). For the oven potatoes, wash the potatoes thoroughly and drain them. Cut the potatoes in half, carve them crosswise, season with salt and pepper and mix with 4-5 tablespoons of olive oil.
Place the potatoes with the cut surface on a baking tray and bake in a preheated oven (electric range: 200 °C/ convection oven: 175 °C/ gas: level 3) for 30-40 minutes. Arrange the rabbits with the braising stock in a deep bowl.
Add extra potatoes.