Mix beef, ricotta, egg, breadcrumbs, half the Parmesan, 1/2 teaspoon salt and oregano just until combined. Refrigerate for 20 minutes, then shape into 12 equal meatballs.
Heat 1 tablespoon olive oil in a saucepan and soften onion for 5 minutes. Add garlic for 30 seconds, then tomatoes, balsamic and remaining salt; simmer uncovered for 20 to 25 minutes until thick, crushing the tomatoes with a spoon.
Preheat air fryer to 375°F and brush the basket with the measured teaspoon oil. Cook six meatballs in one layer for 14 to 18 minutes, turning halfway, until their centers reach 160°F; repeat with the remaining six.
Turn the cooked meatballs in the hot tomato sauce and keep warm. Split the ciabatta rolls and toast their cut faces under the broiler for 1 to 2 minutes.
Place three meatballs along each roll with a restrained spoonful of sauce. Add mozzarella and the remaining Parmesan, then broil for 2 to 3 minutes until melted.
Rest for 2 minutes and close the rolls around the filling. Serve one sandwich per person immediately.