In a large bowl, combine ground chuck, eggs, crumbs, milk, onion, salt and pepper; mix thoroughly. Shape into twelve 3-in. rolls.
Cut steak into twelve 6-1/2-in. x 3-1/2-in. pieces. Wrap each roll in a piece of steak; secure with toothpicks. In a large skillet, brown roll-ups in oil over medium heat.
Spread 2 cups of spaghetti sauce into a 13-in. x 9-in. baking dish. Place roll-ups over sauce; cover with remaining sauce. Cover and bake at 350° for 50-55 minutes or until steak is tender. Remove toothpicks. Serve over pasta if desired.