Stir together butter and Parmesan cheese.
Spread on 1 side of each bread slice.
Place 8 bread slices, buttered side down, on wax paper.
Layer the bread with 2 provolone cheese slices and top with remaining bread slices, buttered side up.
Cook sandwiches in batches on a non-stick skillet over medium heat, gently pressing with a spatula for 3 minutes on each side or until golden brown and cheese melts.
Cut each sandwich in fourths, and serve with warmed marinara sauce.