Spread butter thinly over one side of each bread slice, reaching the edges.
Place 2 slices butter-side down and divide the American cheese evenly over them, folding slices only as needed to fit within the bread.
Close with the remaining bread, butter-side out. Heat a large nonstick skillet over medium-low heat for 2 minutes.
Cook both sandwiches for 3 to 4 minutes until golden underneath. Turn carefully; cook 3 to 4 minutes more until golden on the second side and cheese fully melts.
Rest on a board for 1 minute, cut each sandwich diagonally and serve one per person.