For the meatballs: Preheat the oven to 450 degrees F.
In a bowl, combine the ground beef and breadcrumbs. Add the milk, onion, parsley, salt, pepper, garlic and egg. Mix to combine.
Scoop out 2 tablespoons of the meatball mixture and roll into a ball. Continue with the remaining meatball mixture, making about 40 meatballs. Arrange the meatballs in a single layer in a large rectangular baking dish or foil pan. Bake, uncovered, until the meatballs are cooked through, about 25 minutes.
Pour the marina over the meatballs, then continue to bake until the sauce is heated through, about 10 minutes more. Toss the meatballs to coat in the sauce and set aside.
For the rolls: Turn the oven temperature down to 375 degrees F.
Stir together the butter and garlic in a small bowl. Tear off the tops of the rolls, creating a nice boat to hold the meatballs. Transfer the rolls and torn pieces to a baking sheet and brush generously with the garlic butter. Bake until golden brown, about 10 minutes.
Build the meatball subs: Load 5 meatballs into each roll. Spoon over some of the sauce. Top with some onions and sprinkle over the basil and Parmesan. Serve with more sauce and the toasted bread pieces.
Reheating instructions: Reheat the meatballs in a pan, covered, at 350 degrees F until warmed through, about 25 minutes.