Heat the olive oil in a large skillet on medium heat. Add the onion, carrots, celery, and parsley. Stir to coat with the oil, reduce the heat to low, and cover the pan. Cook until the vegetables are soft and cooked through, 15 to 20 minutes.

Remove the cover, add the garlic, and increase the heat to medium-high. Cook the garlic for half a minute, then add the tomatoes (if using whole canned tomatoes, break up with your fingers as you add them to the pan). Add the basil and tomato paste. Season with salt and pepper.

Bring to a low simmer, reduce the heat to low, and let cook uncovered until thickened while you prepare the meatballs, 15 to 30 minutes.

Purée in a blender, or push through a food mill if you'd like a smooth consistency. Return to the pan and adjust the seasonings.

To make the meatballs, heat the milk in a small pot until steamy. Turn off the heat, tear the bread into little pieces and soak it in the milk until it partially dissolves. Mash it until you get something that resembles a paste. Turn it out onto a plate to let it cool.

In a large bowl, combine the beef, pork, ricotta cheese, grated Parmesan, eggs, garlic, parsley, oregano, salt, pepper, and the bread-milk mixture. Mix it well with your hands until it barely combines.

Don't overwork the mixture or it will become tough. It is OK to have some discernible bits of bread or meat in the mix; better that than overworked meatballs.

Wet your hands and form the meatballs. A traditional size for this sort of meatball is 2 to 3 inches across, but you can make them any size you want.

Once you roll the meatball in your hands, roll it in the flour to give it a good coating. Set each one on a baking sheet as you work. You might need to rinse your hands a few times as you make the meatballs.

When all the meatballs are formed, heat the olive oil in a large skillet over medium-high heat. Brown the meatballs on at least 2 sides. Don't worry about the center getting cooked through, as you will finish these in the sauce.

Once all the meatballs are browned, arrange them in the sauce, turning each one over in the sauce to coat.

Cover the pot and simmer gently for 15 to 20 minutes. Serve with the sauce and pasta or crusty bread. Sprinkle with a little chopped parsley for garnish if you want.