Remove prime rib from the refrigerator. Let it reach room temperature for at least one hour.
Preheat oven to 450°F.
Season prime rib with salt and pepper.
Place in oven and roast for 30 minutes.
Reduce oven temperature to 325°F. Continue roasting for another 2 – 2 1/2 hours, until internal temperature is at least 130°F.
Remove from oven to a cutting board.
Thinly slice prime rib.
Place a large sauté over medium heat. Add 1 tablespoon butter. Allow to melt and get hot, but do not burn.
When hot, add slices from 1 onion and all mushrooms. Sauté until onions are tender and translucent. Remove from heat and set aside.
Clean and oil your grill grates with cooking spray.
Close the grill lid and heat to 550°F.
Form the ground meat into four equal-sized half-pound patties. Season with salt and pepper.
Place burgers on grill and cook to your liking.
Spread butter on both sides of burger buns evenly. Place on grill for one minute to toast.
In the final minute of grilling, top each burger with sliced Swiss cheese.
Remove burgers and buns from grill.
Spread 2 ounces horseradish sauce on the top buns.
Place perfectly grilled burger on bottom bun, cheese side up.
Top with 1/4 of the shaved prime rib.
Add sautéed onion and mushroom mixture, lettuce, tomato slices, raw red onion slices - or any of your other favorite toppings.
Serve immediately.