In a large bowl, mix together ground beef, bread crumbs, cheese, egg, parsley flakes, garlic, salt and pepper. Form into 12 meatballs (about 1/4 cup mixture each).
In a large nonstick skillet, heat oil over medium heat until shimmering slightly. Add meatballs; brown on all sides, 8 to 10 minutes. Remove to a baking sheet lined with paper towels.
Place sauce in a large pot and bring to a simmer over medium-high heat. Add meatballs and simmer, covered, on medium-low heat for 30 minutes. Stir occasionally.
Serve over hot pasta, with additional grated cheese, if desired.