Set oven control to broil. Place butter in small microwavable bowl; cover with microwavable paper towel. Microwave on High 30 to 50 seconds or until melted. Brush butter on 1 side of each bread slice.
On ungreased cookie sheet, place 12 bread slices, buttered sides down. Top each with 1 slice Cheddar cheese and 1 quarter-slice American cheese. Add remaining bread slices, buttered sides up.
Broil with tops 4 to 6 inches from heat 2 minutes. Turn sandwiches over. Broil about 1 minute longer or until golden brown and cheese is melted.