1Cook bacon in 4-quart Dutch oven over medium heat, stirring occasionally, until crisp. Remove bacon with slotted spoon, reserving fat in Dutch oven, and drain on paper towels.
2Mix flour, salt, pepper and paprika. Coat rabbit pieces with flour mixture. Heat bacon fat over medium heat. Cook rabbit in bacon fat about 15 minutes or until brown on all sides.
3Stir in mushrooms, onions, thyme and bay leaf. Pour stout over rabbit and vegetables. Crumble reserved bacon over mixture. Heat to boiling; reduce heat. Cover and simmer about 1 hour or until thickest pieces of rabbit are tender.
4Remove rabbit and vegetables to warm platter; keep warm. Remove bay leaf. Heat stout mixture to boiling. Mix cornstarch and water; stir into stout mixture. Boil and stir 1 minute. Pour sauce over rabbit and vegetables. Sprinkle with parsley.