Bracciole (Flank Steak Rolls)

Heat 2 tablespoons olive oil in a large skillet over medium heat; cook and stir onion in the hot oil until tender, about 10 minutes. Season with 1 teaspoon salt and 1 teaspoon pepper. Mix parsley, garlic, Parmesan cheese, egg, 1 pinch salt, and 1 pinch pepper in a bowl; drizzle in about 1 tablespoon olive oil, while continually stirring, until a sticky consistency is reached. Spread parsley filling in a thin layer atop flank steak; roll steak in a jelly-roll style and fasten ending piece to steak with toothpicks to contain filling. Pour remaining 1 tablespoon olive oil into skillet with onions over medium heat; cook steak roll in the onion mixture, turning steak until browned on all sides, 2 to 3 minutes per side. Add tomato sauce, sugar, and chopped tomato to the steak mixture; simmer over very low heat until steak is cooked through and sauce has slightly reduced, 1 to 1 1/2 hours.