David Venable of QVC recommends cooking the steak for these sandwiches on either the grill or at the stove. Make a quick dipping sauce of mayonnaise, horseradish, Worcestershire, and Dijon for the sandwich.
Preheat the oven to 350 degrees F.
Combine the mayonnaise, horseradish, ½ teaspoon salt, ¼ teaspoon pepper, the mustard, and Worcestershire sauce in a small bowl. Whisk until smooth and refrigerate until ready to serve.
Melt the butter in a medium skillet set over medium heat. Add the onions, ½ teaspoon salt, and ¼ teaspoon pepper to the pan. Sauté the onions until browned and caramelized, 15 to 20 minutes, stirring occasionally.
Sprinkle the steaks on both sides with the remaining 2 teaspoons of salt and 1 teaspoon of pepper. Heat the oil in a large oven-proof skillet over medium-high heat. Add the steaks to the pan and sear until browned, 4 to 5 minutes on each side. When second side is browned, place the skillet into the oven. After 5 minutes, flip the steaks and continue to cook until the internal temperature has reached 135 degrees F (medium-rare) or 140 degrees F (medium), 10 to 15 minutes. Remove the pan from the oven, cover the steaks with foil, and let them rest for 5 minutes.
While the steaks are resting, place the rolls on a baking sheet cut-side up, and divide the cheese among the rolls. Then divide the caramelized onions among the rolls. Place the rolls into the oven and bake until the cheese melts, 5 to 8 minutes.
When the steaks finish resting, transfer them to a cutting board and thinly slice against the grain. Divide the meat among the rolls and top with about 1 tablespoon of the horseradish sauce.