Using your hands and working quickly, combine meat, bread crumbs, grated cheese, parsley, garlic, egg, salt, and pepper in a bowl.
In a pan with sides tall enough for deep-frying, heat 1 cup oil to 360 degrees F. While the oil is heating, form meat mixture into little balls no more than 3/4-inch in diameter. When oil is hot, add the meatballs, a few at a time, and fry until brown on all sides. As they finish cooking, set aside to drain on paper towels.
Gently stew the tomatoes and onion in 2 tablespoons oil in a saucepan over medium heat, crushing tomatoes with a fork as they cook, until most of the liquid has evaporated and the sauce is dense. Taste and add salt, if necessary. Transfer to a food processor or food mill and process briefly to make a smooth puree.
Return puree to the pan, add drained meatballs, and let bubble over medium-low heat for 2 to 3 minutes to absorb flavors. Just before serving, stir in fresh herbs.