In a large bowl, combine the first six ingredients; mix well. Shape into 12 thin patties. Broil 4 inches from the heat for 7-8 minutes on each side or until no longer pink. In a small bowl, combine cheese, mayonnaise, mustard and relish; mix well. Sp oon 2 tablespoons on each burger. Return to the broiler just until cheese softens. Place lettuce and onion on bottom of buns; top each with two burgers, tomato and top of bun.