With the rack in the highest position, preheat the oven’s broiler.
In a large non-stick skillet, sauté the onions in the oil over medium heat for about 10 minutes or until they caramelize. Season with salt and pepper. Add the broth and meatballs. Cover and simmer gently for about 5 minutes, until the meatballs are warmed through. Uncover and reduce the broth until almost dry.
Meanwhile, place the rolls, cut open, on a baking sheet. Brown the rolls on each side in the oven.
Spread the inside of the rolls with the mustard and mayonnaise. Cover with cheese and melt in the oven. Fill with the meatball and onion mixture. If desired, garnish with chopped iceberg lettuce. Close.