In a large saute pan or griddle, heat the oil over medium-high heat for 1 minute, and then add the onions, 1 tablespoon salt and 1 teaspoon pepper. Cook the onions until caramelized, stirring throughout the process, 5 to 6 minutes. Remove and keep warm.
Spread the softened butter on the interiors of the rolls and cook, butter-side down, on a griddle until browned, 1 to 2 minutes. Remove the rolls, add the raw steak to the griddle and sprinkle with salt and pepper. Cook briefly, shredding the meat into small pieces with two metal spatulas. Add the onions and cook for 2 minutes.
Portion the meat into four piles, and top each pile with 3 slices of the provolone. Continue to cook until the cheese melts (putting on the lid and adding a little water to the pan can help with this step). Cover each pile with a browned roll, and slide a spatula under the meat to pick it up with the roll.