Stir together butter and Parmesan cheese; spread on 1 side of each bread slice. Place 8 bread slices, buttered sides down, on wax paper.
Layer 8 bread slices on wax paper each with 2 provolone cheese slices, and 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, 3 minutes on each side or until golden brown and cheese melts. Cut each sandwich into fourths, and serve with marinara sauce for dipping.