Step 1

Arrange bread in a single layer on a clean work surface. Stir together butter and mayonnaise. Spread mixture evenly onto one side of every slice (1 scant tablespoon per slice).

Step 2

Heat a large skillet, preferably cast iron, over medium. Flip over bread on work surface (so it's plain-side up). Place 1 1/2 slices American cheese on 4 slices, and 1/4 cup cheddar on remaining 4 slices. Carefully sandwich together.

Step 3

Place sandwiches in skillet (in two batches, if needed). Reduce heat to medium-low; gently top sandwiches with a lid slightly smaller than skillet for even cooking. Cook, flipping once halfway through, until crisp and golden on both sides and cheese is melted, 7 to 9 minutes. Serve immediately.