In a large cast-iron casserole, heat the olive oil until just smoking. Add the rabbit and brown well on all sides. Season the meat with salt and pepper, remove from the casserole and set aside.
To the same casserole, add the garlic and reduce heat to medium. Cook garlic 1 to 2 minutes, until it is softened but not browned. Add the tomatoes, tomato paste, rosemary and wine and simmer 5 minutes.
Return the rabbit to the casserole, cover loosely and cook over low heat for 1 hour, until meat is very tender. In a small bowl, combine the liver and the vinegar and mash well with a fork. Add the liver mixture to the casserole and cook 10 minutes. Add the basil leaves, remove from heat and serve immediately.