Grate the bread into coarse crumbs on the large holes of a box grater; put in a large bowl. Add the milk and set aside for 5 minutes to allow the bread to soak up the milk. Add the beef, Parmesan, parsley, onion, garlic, egg, 1 teaspoon salt and a few grinds of pepper; mix until just combined. Shape the meat mixture into 18 meatballs, working a piece of mozzarella into the center of each and making sure it?s completely covered. Refrigerate for at least 2 hours or up to overnight.
Bring the marinara sauce to a very light simmer in a large Dutch oven or large wide pot. Heat half of the oil in a large nonstick skillet over medium-high heat. Working in batches, add the meatballs and cook, turning occasionally and adding the remaining oil as needed, until browned on all sides, about 6 minutes. Transfer the meatballs to the marinara sauce as they are browned.
Bring the sauce to a boil, lower the heat, and simmer, covered, gently stirring occasionally, until the meatballs are cooked through, about 15 minutes. Remove from the heat and stir in the basil. Adjust the seasoning with additional salt and pepper. Serve over hot pasta.
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