In a medium bowl, combine the ground beef, egg, bread crumbs, 2 tablespoons of parsley, salt, and pepper. Mix well.
Pinch off a ball of the mixture, roll between your hands to make ping pong ball-sized meatball. Repeat with the rest of the meat.
In a large pan, cook the meatballs over medium heat, turning to brown each side. Remove from heat and drain on a paper towel.
Preheat oven to 350°F (180˚C).
Pinch off a portion of pizza dough and, with your hands or a rolling pin, flatten out and top with a tablespoon of marinara sauce and mozzarella cheese. Add a meatball and wrap the dough over, pinching at the seams to close. Repeat with the remaining ingredients.
Arrange the balls in a circle, seam-side down, in a large cast-iron skillet.
Mix the melted butter with the garlic, remaining 2 tablespoons of parsley, and the Parmesan. Brush the balls with the garlic butter mixture.
Bake for 20 minutes, or until golden brown. Let cool for 5-10 minutes.
Place a bowl of warm marinara sauce in the middle of the skillet, then serve.