Place the leg of kid, one tablespoon of the butter and the olive oil in a Dutch oven. Brown meat slowly but thoroughly on all sides. When brown, remove to a dish and keep warm.
Place the onion, carrot, water, celery, parsley and remaining butter in the Dutch oven. Brown vegetables well without burning, adding a little more water if necessary.
Arrange the kid over the braised vegetables and pour over it any juice that drained from it while it was standing. Add the salt, pepper and wine. Cook until wine evaporates. Add the stock. Cover and cook slowly for two hours, or until meat is tender.