Spread 2 tablespoons pasta sauce evenly over each square, leaving a 1/2-inch border. Spoon 1/2 cup ham mixture onto each square, and sprinkle each with 1 tablespoon mozzarella cheese. Fold the dough over the filling to form a triangle, pressing edges to seal.
Place calzones on a baking sheet coated with cooking spray. Press edges with a fork to seal. Coat tops of calzones with cooking spray; sprinkle with Parmesan cheese.