In a large skillet cook onion in the 4 teaspoons hot oil over medium heat about 10 minutes or until golden brown; stir occasionally. Stir in salt and 1/4 teaspoon pepper. Cover; keep warm.
Meanwhile, in a large bowl combine beef, Worcestershire sauce, the 1/2 teaspoon pepper, and the garlic. Divide into eight equal portions. Shape each portion into a 4-inch diameter patty. Place one-fourth of the cheese on each of four of the patties. Top with remaining patties, pressing down lightly and sealing edges well. Grill patties directly over medium coals for 14 to 18 minutes or until done (160 degree F), turning once halfway through grilling. (Or, place patties on the unheated rack of a broiler pan. Broil 3 to 4 inches from heat for 14 to 18 minutes or until done, turning once halfway through broiling.)
Brush bread slices lightly with the 1 tablespoon olive oil. Add bread slices to grill rack or broiler pan the last 2 to 3 minutes of cooking time or until toasted, turning once. To serve, place patty on a toasted French bread slice; top with onion mixture. Makes 4 sandwiches.