In a large bowl, gently combine the onion, beef, tomato paste, bread crumbs, Cheddar, egg, 1 1/2 teaspoons salt, and 1/2 teaspoon pepper. Shape into 20 meatballs.
Heat the oil in a large saucepan over medium heat. Add the meatballs and brown on all sides, about 7 minutes total. Add the sauce to the pan and bring to a boil. Reduce heat and simmer 5 to 6 minutes, until the meatballs are cooked through. Divide the meatballs and sauce among individual plates.