To prepare meatballs, place bread cubes in a bowl. Pour milk overtop, Soak for 15 minutes. Drain and squeeze out extra moisture. Add ground beef, onion, garlic, egg, cheese, parsley, salt and pepper. Mix using your hands. Meanwhile, preheat oven to 350° F. Divide mixture into 12 portions. With wet hands, form a portion into a patty, then push a cube of mozzarella into the centre and form meat into a ball around the cheese. Repeat with the remaining meat and cheese. Place on a parchment-lined baking sheet.
Coat a large skillet with oil and set over high heat. Add meatballs. Cook for about 10 minutes, turning often. Carefully add meatballs to sauce in ovenproof pot. Bake for about 10 minutes. Remove from oven.
Boil spaghettini in salted water until al dente. Drain well. Add to tomato sauce and meatballs. Gently stir. Divide among dishes. Top with grated Parmesan.