Spread the butter on one side of each bread slice. Add a slice of cheddar and a slice of mozzarella on each piece of bread, then cover with another bread slice, buttered-side up. Sprinkle Parmesan cheese on the outside of one side of the sandwich.

Heat a large skillet over medium heat. Place the sandwich, cheese side down, on the hot pan. Grill for 2 minutes or until Parmesan cheese is crusted and golden brown. Sprinkle Parmesan cheese on the outside of the other side of the sandwich. Cook until golden brown and the cheese has melted, about 2 more minutes. Serve immediately.