Thinly and evenly spread mayonnaise or softened butter on both sides of the bread slices. Or melt the butter and brush it on.
Place 2 pieces of bread, buttered side down in a frying pan over medium heat. Toast on first side. Remove them from the skillet.
Pat the ham dry with paper towels to remove extra moisture. Top the toasted side of the bread with 2 slices of the cheddar cheese, then top the cheese with 1/4 of the ham. Lay 2 pieces of the American cheese on top of the ham.
Place the second piece of bread on top of the sandwich, with the browned side towards the inside of the sandwich. Place sandwiches in a large cast-iron skillet over medium to medium-low heat.
When the sizzling slows down or nearly stops, the bread has finished releasing moisture and is ready to flip. When sandwiches are golden brown, carefully flip with a spatula, so you don't lose ingredients. Be careful not to burn the bread. Top the pan with a lid so that cheese melts nicely.
Repeat until you have 4 sandwiches.
Let cool slightly before serving.
Can be kept warm in the oven on low heat, until all sandwiches are toasted.
Video
Notes
When the sizzling slows down or nearly stops, the bread has finished releasing moisture and is ready to flip.Best if eaten fresh.Do not freeze.See post above for bread and accompaniment suggestions.