Melt butter and stir in the parmesan cheese.

Make the sandwich with a slice of white cheddar and about 1/4 cup shredded mozzarella cheese. (Or if your mozzarella is sliced instead of shredded, put one slice of American or cheddar between 2 slices of mozzarella) Brush one side of the sandwich with the melted butter. Place the sandwich buttered side down in a hot pan and brush the top side with more melted butter.

Grill until brown and toasty on the underside. Flip sandwich. Grill until both sides are brown and toasty. Lower heat when you flip the sandwich so that the bread doesn't get too dark before the cheese melts.