When the oil is hot, add the onions and peppers. Season with salt and pepper. Saute the vegetables for 2 to 3 minutes. Season the steak with salt and pepper and add to the vegetables, saute for 2 to 3 minutes. Using a spatula, divide the sauteed mixture into fourths. Place two slices of cheese on top of each fourth of the sauteed mixture. Spread both halves of the bread with mayonnaise. Using a spatula, remove each fourth and place on each individual bun. Wrap each sandwich in foil and keep warm.
Lay the potatoes in the hot oil and fry until golden-brown, about 3 to 4 minutes. Remove from the oil and drain on a paper-lined plate. Season the fries with salt and pepper. Make a pocket out of foil for the fries. Serve the steak sandwiches and fries together.
This recipe yields 4 sandwiches.