1. Serves 12.
Cook the Caramelized Red Onions: Melt butter in a large, heavy-bottomed pan over medium-low heat. Cook onions, stirring often, for 60 to 90 minutes or until golden brown. Season with salt. Cool completely.
2. Assemble the sandwiches: Butter outer bread slices. Spread 1 tablespoon mustard between two slices of bread. Pile on 3 ounces of apple slices (about ½ of one apple), 1 slice of cheese and ¼ cup caramelized onions. Cook sandwich over medium-low heat until golden brown on each side and cheese is melted. Cut in half before serving. Repeat to make the rest of the sandwiches.