Preheat oven to 325°F. Season the rabbit pieces with salt and pepper. Add the flour to a paper bag. Put the rabbit pieces in the bag. Seal it and shake to evenly coat the rabbit with flour.
Heat 2 tbsp. oil in a large, lidded skillet or Dutch oven over medium heat. Add the onions, shallots, and carrots to the pan and sauté for 2-3 minutes until slightly soft.
Add the leeks and garlic and sauté for 1 minute. Add mushrooms and sautee for 2 minutes. Transfer vegetables to a bowl and set aside.
Place the rabbit pieces in the skillet or Dutch oven and brown on each side. Return the vegetables to the pan. Pour in the wine or vermouth stir and cook for 1-2 minutes until wine is slightly reduced. Add the rabbit stock, tomato paste, and tomatoes. Stir to combine.
Add the herbs and black pepper. Stir to combine. Bring to a boil then reduce to a simmer. Turn off stovetop heat. Add potatoes to top of mixture and stir. Cover and place in the oven. Cook for 1 hour. You may cook longer if you like up to 2 hours. The meat should be tender.
When there is 20 minutes left to your cook time, remove from oven and add the olives and chopped rabbit liver. Put the lid back on the pan and return to the oven to finish cooking.