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 non-stick skillet over medium heat,
gently pressing with a spatula, 4 minutes on each side or until golden brown and cheese is melted.