Step 1

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

Step 2

Grate 3 ounces American cheese and 3 ounces provolone cheese on the large holes of a box grater (about 1/2 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 1/2 cups). Thinly slice 1 (1 1/2-pound) boneless ribeye steak across the grain into very thin (1/4-inch-thick) strips. Season the steak with 1/2 teaspoon of the kosher salt and 1/4 teaspoon of the black pepper.

Step 3

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.

Step 4

Add the remaining 1 tablespoon olive oil to the now-empty skillet. Add the bell peppers, onion, remaining 1/2 teaspoon kosher salt, and remaining 1/4 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.

Step 5

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.