Combine butter, parsley, Pecorino Romano cheese, and garlic in a small bowl. Stir to combine.
Lightly coat 1 side of each bread slice with the butter mixture. Flip bread and top 2 slices evenly with provolone cheese and mozzarella cheese. Cover with remaining bread slices, buttered-sides up.
Place sandwiches into the hot skillet. Cook until golden brown on one side, 3 to 4 minutes. Flip and cook until golden brown on the second side and cheese has melted, 3 to 4 minutes more. Cut each sandwich in half and serve.