Preheat the skillet or griddle over medium heat.
In a small bowl, mix the horseradish sauce with a pinch of salt and pepper. Set aside.
Slice the sandwich rolls in half horizontally.
Arrange the thinly sliced prime rib on the bottom halves of each roll. If desired, add a slice of cheese on top of the meat.
Spread a generous amount of horseradish sauce over the prime rib.
Top with a handful of fresh arugula.
Close the sandwiches with the top halves of the rolls.
Drizzle olive oil on the skillet or griddle. Place the sandwiches on the skillet and grill for about 3-4 minutes on each side, or until the bread is golden brown and crispy, and the cheese is melted (if using).
Once grilled, remove sandwiches from the skillet, slice them in half if desired, and serve immediately.
Feel free to customize the sandwich with your favorite toppings like sautéed onions or peppers, or a spicy mustard.