In a large skillet cook ground beef, onion, and garlic till meat is brown and onion is tender. Drain off fat.
Meanwhile, in a 3 1/2- or 4-quart crockery cooker combine tomato juice; catsup; water; brown sugar; jalapeño peppers, if desired; mustard, chili powder; and Worcestershire sauce. Stir in meat mixture. Cover; cook on low-heat setting for 10 to 12 hours or high-heat setting for 3 to 5 hours. Toast buns; spoon meat mixture over buns and sprinkle with cheese.