To make the tomato sauce: Heat 2 tablespoons olive oil in a large skillet over medium heat. Add 1 small onion, finely chopped, 1 small carrot, finely chopped, and 1 small celery rib with leaves, finely chopped. Cover, reduce the heat to low, and cook, stirring occasionally, until the vegetables are very soft, about 15 minutes.
Add 2 garlic cloves, minced, and 1 tablespoon chopped basil, rosemary, sage, or thyme. Cook, stirring, for 30 seconds.
Stir in 2 pounds fresh plum or Roma tomatoes, peeled and coarsely chopped or one 28-ounce can whole tomatoes, ½ cup sun-dried tomatoes, soaked in boiling water until soft, and finely chopped, 2 teaspoons tomato paste, ¾ teaspoon salt, or to taste, and ¼ teaspoon black pepper, or to taste. Simmer, uncovered, crushing the tomatoes with a potato masher or a wooden spoon to break them up, until the sauce is thickened, 15 to 20 minutes. Pass through a food mill for a smooth sauce. Bring tomato sauce to a low simmer, cover, and have at the ready.
For the meatballs:
Combine the following into a large bowl:
1 pound ground beef, half ground beef and ground
pork, or 12 ounces lean ground beef and 4 ounces hot
or mild Italian sausage, removed from its castings
2 garlic cloves, minced
½ cup chopped parsley
½ cup grated Parmesan (2 ounces)
1 medium onion, finely chopped
½ cup bread crumbs
1 large egg, beaten
3 tablespoons dry red wine
2 tablespoons tomato paste
1 teaspoon salt
¼ teaspoon black pepper
½ teaspoon dried oregano
Mix with your hands. Scoop out the mixture in heaping tablespoons and form into 1½-inch balls. Dredge the meatballs in ½ cup flour.
Heat ¼ inch olive or vegetable oil in a large skillet over medium heat. When the oil shimmers, fry the meatballs in uncrowded batches, turning them several times so that they brown evenly. As the meatballs finish browning, transfer them to the warmed tomato sauce, if using. If not serving with a sauce, place the browned meatballs in a baking dish and transfer to oven to keep warm.