Place the anchovies, bread crumbs, Parmigiano cheese, parsley, garlic, egg, salt, and wine in a mixing bowl. Combine the ingredients together well, using your hands. If the mixture is too dry, add more wine, or if it's too wet, add more bread crumbs. Scoop the mixture, about the size of an egg, onto the palm of your hands and form into a compact ball. Repeat with the remaining mixture.
Heat up extra-virgin olive oil in a deep heavy-bottomed pan. Gently place the balls in the hot oil, a few at time, and fry until golden brown. Turn the balls over to cook on all sides. Transfer to a plate lined with an absorbent paper towel. Serve immediately or place into simmering tomato sauce for a few minutes. Serve with tomato extra sauce.
Sauce: Heat the olive oil in a saucepan and add the onion, garlic, and chile peppers. Gently fry ingredients together, about 5 minutes.
Add pureed plum tomatoes to saucepan. Simmer on low to medium heat for 10 minutes. Season with salt, to taste. Add basil leaves at the very end.