Preheat broiler; coat broiler pan with cooking spray.
Combine 2 tablespoons sauce and chicken in a medium bowl, tossing to coat. Arrange chicken in a single layer on broiler pan; broil 4 minutes on each side or until done.
Place chicken in a bowl; toss with remaining 2 tablespoons sauce.
Combine cheese and mayonnaise.
Spread 3 tablespoons cheese mixture on each of 4 bread slices; top each with one-fourth of cooked chicken and 1 bread slice.
Heat a grill pan over medium-high heat. Coat pan with cooking spray. Arrange 2 sandwiches in pan.
Place a cast-iron or heavy skillet on top of sandwiches; press gently. Cook for 3 minutes on each side or until bread is toasted (leave skillet on sandwiches while they cook). Repeat procedure with remaining 2 sandwiches.
