Preheat oven to 400° and line a baking sheet with parchment. Place a wire rack inside sheet, then spray rack with cooking spray.
In a medium bowl, beat 1 egg to blend. Add beef, onion, Provolone, garlic, parsley, bread crumbs, basil, oregano, salt, pepper, and ½ cup Parmesan and gently stir until combined.
Using a 1 ½-tablespoon cookie scoop or measuring spoon, portion out 1-ounce balls of beef mixture. Working one at a time, flatten with the heel of your palm, place mozzarella in the center, and enclose beef mixture around mozzarella. Arrange meatballs on prepared rack.
Bake meatballs 10 minutes. Transfer meatballs to a plate and let cool. Remove rack, replace parchment, and increase oven temperature to 425°.
Divide dough into 24 (½-ounce) portions. Flatten each with the palm of your hand, then place a meatball in the center. Enclose dough around meatball and transfer to prepared sheet.
In a small bowl, beat remaining egg. Brush tops of dough with egg wash. Sprinkle each with a pinch of remaining Parmesan.
Bake sub bites until dough is golden brown, about 20 minutes. Let cool slightly.
In a small saucepan over medium heat, heat oil. Cook garlic, stirring occasionally, until fragrant and lightly browned, about 3 minutes.
Stir in tomatoes, basil, oregano, Parmesan, salt, and red pepper. Reduce heat to low and cook, uncovered, until sauce is slightly thickened, about 20 minutes.
Arrange sub bites on a platter. Serve with marinara sauce alongside.
