1. In a bowl, mix ground beef, egg, onion, bread crumbs, Worcestershire, garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper until well blended. Divide mixture into four equal portions and shape each into a patty about 4 inches wide.
2. Lay burgers on an oiled barbecue grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill. Cook burgers, turning once, until browned on both sides and no longer pink inside (cut to test), 7 to 8 minutes total. Remove from grill
3. Lay buns, cut side down, on grill and cook until lightly toasted, 30 seconds to 1 minute.
4. Spread mayonnaise and ketchup on bun bottoms. Add lettuce, tomato, burger, onion, and salt and pepper to taste. Set bun tops in place.
Notes: If you want absolute bacteria safety, you need to cook your burgers to 160°. This recipe will keep them moist. To make cheeseburgers, about 1 minute before burgers are done, top with sliced cheese; continue cooking until cheese begins to melt. Prep and cook time: about 30 minutes.