Slice and season the steak: Slice the ribeye against the grain as thinly as you can manage, about 1/8 inch. Season with the salt and pepper and set aside.

Toast the rolls: Spread the softened butter on the cut sides of the hoagie rolls, arrange them cut side up on a sheet pan, and broil for 1-2 minutes until lightly golden. Watch them closely, they go from toasted to burnt fast.

Cook the onion and pepper: Heat 1 tablespoon of the oil in a large skillet or griddle over medium-high heat. Add the onion and bell pepper and cook for 6-7 minutes, stirring occasionally, until soft and browned at the edges. Transfer to a plate.

Sear the steak: Add the remaining 1 tablespoon oil to the same skillet and turn the heat to high. Spread the steak in a single layer and let it sit undisturbed for 2 minutes, then chop and toss it with the edge of a spatula for 2-3 minutes more, just until no pink remains. Thin-shaved beef cooks through in minutes, so pull it the moment the pink is gone or it turns tough.

Pile and melt the cheese: Return the onion and pepper to the skillet and toss with the steak. Push the mixture into 4 roughly roll-sized mounds and lay 2 slices of provolone over each one. Turn off the heat, cover the pan, and let it stand 3 minutes, until the cheese is fully melted. The pan's residual heat does the melting, and those 3 minutes double as the rest the USDA recommends for beef.

Build the sandwiches: Slide a wide spatula under each mound and flip it straight into a toasted roll, cheese side down. Serve right away while everything is hot.