Butter 1 side of each slice of bread. On a nonstick skillet or griddle preheated to medium heat, place ½ of the bread slices buttered-side down; top each slice evenly with ½ cup shredded cheese and 2 slices American cheese. Top cheese with remaining slices of bread, buttered side up. Cook sandwiches on first side until the bottom is dark golden-brown (about 2 min.); flip and repeat. If needed, reduce heat slightly and continue cooking, flipping occasionally, until cheese is melted and hot. Cut each sandwich in half on the diagonal; serve immediately.