Preheat oven to 400 degrees. Unroll dough; separate into 12 breadsticks. Cut each breadstick crosswise in half; flatten dough to 2-inch width.
Spoon 1 teaspoon mozzarella cheese onto center of a ham piece. Fold ham piece over cheese to create a tight roll. Place ham roll near the end of a piece of breadstick dough, leaving a border. Fold dough over ham, pinching edges to seal. Repeat process for all ham pieces. Place calzones on baking sheet. Sprinkle with Parmesan cheese.