Heat 3 tablespoons oil in an ovenproof skillet over medium heat; cook the onions, garlic, and parsley until softened, about 10 minutes. Scrape out onto a plate and allow the mixture to cool; set the pan aside. Pour the milk over the bread into a medium bowl and let it soak while the onions are cooling. Combine the meats in a large bowl and add the egg and Parmesan. Season with salt and pepper. Squeeze the excess milk from the bread and add the bread to the bowl along with the cooled onion mixture. Using your hands, gently combine all the ingredients until they are thoroughly mixed. Don't overmix or the meatballs will be tough. Divide this mixture into 10 pieces and form them into patties. Place a mozzarella cube onto each patty and bring up the sides around the cheese to form a ball completely enclosing the cube.
Preheat the oven to 350 degrees F.
Heat the remaining oil in the skillet over medium heat and brown the meatballs on all sides, about 10 minutes. Put them into the oven and bake until the meatballs are cooked through, about 15 minutes.
Cook the spaghetti in a large pot of boiling salted water until al dente, about 6 to 8 minutes. Drain the pasta and put it onto a large serving platter. Pour on half the Sugo Sauce and mix well. Place the meatballs over the spaghetti and garnish with the basil leaves. Serve immediately along with the extra sauce and Parmesan.
Sugo Sauce for Sergio:
Pour the olive oil into a large skillet over medium heat. Add the onion, garlic, and half the basil and cook until soft, about 10 minutes. Add the olives, capers, and remaining basil. Carefully add the tomatoes (nothing splashes like tomatoes) and about 1/2 cup of the reserved liquid; cook until the sauce is thick, about 15 minutes. Taste and adjust seasoning with salt and pepper.