Grilled Prime Rib Sandwich with Horseradish Cream

Method

1. Remove the prime rib roast from the refrigerator 1 hour before cooking so it comes closer to room temperature, which helps it cook more evenly.
2. Pat the roast completely dry with paper towels, then rub it all over with the olive oil, minced garlic, and chopped rosemary, followed by the coarse salt and pepper pressed into the surface.
3. Set up your grill for indirect heat by lighting burners or charcoal on only one side, aiming for a steady grill temperature of 325F, and place a drip pan on the unlit side.
4. Insert a meat thermometer probe into the thickest part of the roast, avoiding any fat pockets, if your thermometer allows for continuous monitoring.
5. Place the roast on the cool, indirect side of the grill, close the lid, and cook for approximately 1.5 to 2 hours, checking the internal temperature periodically rather than relying only on time.
6. Remove the roast from the grill once the internal temperature reaches 130F for medium-rare, since the temperature will continue climbing another 5 to 10 degrees as it rests.
7. Tent the roast loosely with foil and let it rest for a full 20 minutes without cutting into it, which allows the juices to redistribute through the meat.
8. While the roast rests, whisk together the sour cream, prepared horseradish, and Dijon mustard in a small bowl to make the horseradish cream sauce, then refrigerate until ready to use.
9. Slice the rested roast very thinly against the grain using a sharp carving knife, aiming for slices about 1/8 inch thick.
10. Split the French rolls and toast them lightly, cut-side down, on the grill for about 1 minute until warm and lightly crisp.
11. Spread a generous layer of horseradish cream on both cut sides of each roll, pile on a handful of thinly sliced prime rib, and top with a small handful of arugula before closing the sandwich.