Mix ham and apple with mayonnaise in a small bowl. Spread onto two slices of bread. Top each one with a slice of cheese and a second slice of bread.
Melt butter over medium heat in a large skillet. Whisk together eggs and milk in a small bowl. Quickly dip both sides of the sandwich into the egg mixture. Fry sandwiches in pan for 1 to 2 minutes per side, or until golden brown. Watch carefully. You want the sandwiches to be golden in color and the egg to be cooked.