Stir together butter and Parmesan cheese in a small bowl.
Spread 1 1/2 tsp. butter mixture on 1 side of each bread slice.
Place 4 bread slices, buttered sides down, on wax paper. Top with provolone and mozzarella cheeses; top with remaining bread slices, buttered sides up.
Cook sandwiches, in batches, on a hot griddle or in a nonstick skillet over medium heat, gently pressing with a spatula, 4 minutes on each side or until golden brown and cheese is melted.
