Arrange a rack in the upper third of the oven (about 5 inches from the broiler). Heat the broiler to HIGH.

Grate 3 ounces American cheese and 3 ounces provolone cheese on the large holes of a box grater (about ½ cup each), or cut sliced cheese crosswise into thin slices.

Trim and thinly slice 2 medium bell peppers (about 3 cups).

Thinly slice 1 large yellow onion (about 1 ½ cups).

Thinly slice 1 (1 ½-pound) boneless ribeye steak across the grain into very thin (¼-inch-thick) strips.

Season the steak with ½ teaspoon of the kosher salt and ¼ teaspoon of the black pepper.

Heat 1 tablespoon of the olive oil in a large cast iron or stainless steel skillet over medium-high heat until shimmering.

Add half of the steak in a single layer. Cook without stirring until browned on the bottom, 2 to 3 minutes.

Flip and continue cooking until the steak is browned on the second side and just cooked through, 1 to 2 minutes.

Transfer the steak to a plate and cover with aluminum foil. Repeat cooking the remaining steak.

Add the remaining 1 tablespoon olive oil to the now-empty skillet.

Add the bell peppers, onion, remaining ½ teaspoon kosher salt, and remaining ¼ teaspoon black pepper.

Cook, stirring occasionally, until the onions are tender and browned and the bell peppers are tender, 5 to 7 minutes.

Turn off the heat.

Return the steak to the skillet and toss with the peppers and onions.

Top evenly with the cheese.

Broil until the cheese is melted and browned in spots, 2 to 3 minutes.

If using sandwich rolls, cut lengthwise down the center of 4 rolls, but do not cut all the way through.

Pull out and discard some of the soft interior of the bread, then stuff the rolls with the cheesesteak filling.