Heat 3 tablespoons oil in a nonstick skillet over high heat. Saute the onion slices until wilted and just starting to take on some color, stirring all the while, about 7 minutes. Sprinkle onions with salt while cooking.
Slice the top round into very thin slices. Partially freezing the meat enables you to slice it very thinly.
Remove the onions from the skillet. Salt and pepper the steak slices and then saute them in the same skillet, in batches until cooked through, about 45 seconds per side. Repeat process for the remaining steak slices, replenishing oil as needed.
Meanwhile, melt the cheese cubes in a microwave-safe bowl on low power for a couple minutes or until completely melted.
Cut each roll down the middle lengthwise. Fill each roll with a good helping of steak slices and top with the melted cheese and sauteed onions.