1. To prepare horseradish mayonnaise: combine mayonnaise, horseradish and garlic pepper in small bowl and stir to blend. Taste and adjust seasoning, if desired.
2. To prepare caramelized onions: heat oil in a large skillet over medium heat; add onions, salt and black pepper. Cook for 2 to 3 minutes, stirring frequently, or until onions are wilted. Reduce heat to medium-low and cook for 15 to 20 minutes, stirring frequently, or until onions are golden and lightly caramelized.
3. Meanwhile, heat a cast iron skillet over high heat until very hot (about 5 minutes). Remove excess moisture on steak with paper towels; season steak generously with salt and black pepper. Add oil to hot skillet; heat until just beginning to smoke. Carefully add steak and cook over high heat for 3 to 4 minutes, or until a golden-brown crust forms. Turn steak over and cook an additional 2 minutes.
4. Reduce heat to medium; add butter. Carefully tilt skillet slightly and spoon foamy butter over steak for 2 to 3 minutes, or to desired doneness. Transfer steak to a plate; cover loosely with foil and let rest for 5 minutes. Thinly slice steak against the grain.
5. To assemble sandwiches: Spread horseradish mayonnaise over cuts sides of rolls. Arrange lettuce on bottom halves of rolls; top each evenly with sliced steak, shredded Cheddar cheese and 1 tablespoon caramelized onions. Close with top halves of rolls.