Chill steak in the freezer for 30 minutes until firm but not frozen solid. Slice across the grain as thinly as possible with a sharp knife, about 1/8 inch or less. Separate any slices that cling together and pat away surface moisture.

Split rolls without cutting completely through. Lightly butter the cut sides and toast in a dry skillet or under a broiler until golden, watching continuously under the broiler. Set aside while preparing the filling.

Heat 1 tablespoon oil in a wide skillet over medium heat. Cook onion and bell pepper 10–12 minutes, stirring, until tender and golden. Transfer to a bowl. Raise heat to medium-high and add remaining oil.

Cook steak in two batches in a single layer, about 2–3 minutes per batch, turning and separating the thin slices. Season with salt and pepper. Work quickly but ensure the meat reaches 145°F (63°C), then allow a 3-minute rest before eating. Avoid overloading the pan, which makes the filling watery.

Return onions, pepper and steak to the pan over low heat. Divide into four portions and lay two slices provolone on each. Cover briefly, 30–60 seconds, until melted. Slide each portion into a toasted roll and serve warm. The listed 30-minute chilling time is separate from active preparation.