Prepare the sauce: Blend carrot, onion, and celery with some olive oil. Use half for the sauce base and half for the meatball mix. Cook the soffrito with olive oil, then add the tomato sauce, salt, and pepper. Cover and simmer on medium-low heat for 1 hour, stirring every 15 minutes.
Make the meatball mix: Combine pork and veal. Soak bread in warm water, then squeeze out moisture. Mix meat with the soffrito, cheese, bread crumbs, salt, egg, crushed garlic, and parsley. Mix thoroughly.
Shape and cook meatballs: Form meatballs (about 40g each), keeping hands wet to prevent sticking. Bake at 180°C (356°F) for 20 minutes or shallow fry until cooked.
Finish cooking in sauce: Add basil to the sauce, then gently place meatballs in. Cover and simmer for 30-40 minutes, stirring carefully if needed.
Serve: Serve meatballs with sauce, garnished with parsley, cheese, and basil leaves.