Melt 1 teaspoon of butter in a pan set over medium heat. Add the onions and sugar. Cook, stirring frequently, until soft and deeply browned – about 30 minutes. (Make ahead tip: freeze a big batch of caramelized onions in an ice cube tray!)

Arrange four slices of bread on a flat surface. Top each with 3 pieces of American, some of the caramelized onions, apple slices, and bacon (if using). Top each sandwich with a second slice of bread.

Heat one piece of butter on a griddle set over medium low heat. Add two sandwiches. Cover and cook 3 minutes. Add a second piece of butter. Flip the sandwiches and cook uncovered for another 3-4 minutes, until the bread is golden brown and toasted and the cheese is melted. Repeat with the remaining sandwiches.

Cut on a diagonal and serve hot.