Soak the breadcrumbs and milk in a large bowl for 5 minutes. Add the beef, egg, garlic, Parmesan, parsley, salt, and pepper. Mix gently with your hands until just combined.

Shape the mixture into 12 to 16 golf ball size meatballs. Heat the olive oil in a large skillet over medium-high heat. Brown the meatballs in batches on all sides, about 6 to 8 minutes per batch. Transfer to a plate.

Pour the marinara into the same skillet, scraping up browned bits. Return the meatballs, spoon sauce over them, and bring to a simmer. Reduce heat to low, cover, and cook until the meatballs reach 160°F, 25 to 30 minutes.

Meanwhile, preheat the broiler. Split the rolls and place them cut side up on a baking sheet. Broil until lightly golden, 1 to 2 minutes. Top with mozzarella and broil until melted, another 1 to 2 minutes.

Use a slotted spoon to place 3 or 4 meatballs on each roll bottom. Ladle a little sauce over them, close the sandwich, and serve immediately with fresh basil if desired.