Pat the roast dry with paper towels. Season all over with the salt. Place on a wire rack set over a rimmed baking sheet. You can refrigerate at this point, uncovered for up to 3 days. When ready, bring the prime rib to room temperature for about 2-3 hours before cooking. This allows the meat to cook evenly.
Preheat: Position a rack in the lower third of the oven and preheat to 500°F.
Make the butter: In a small bowl, mix together the butter, garlic, salt, pepper, rosemary, and thyme. Spread evenly over the top and sides of the roast.
Place the roast bone-side down in a roasting pan or on a rack if using boneless. Insert a leave-in probe thermometer into the thickest part, not touching bone.
Roast at 500°F for 20 minutes. Reduce heat to 325°F and roast for around 13-20 minutes per pound. Cook by internal temperature not time. Time is just a general guideline. Roast is done when the center reaches 120°F for medium-rare (or desired doneness - see temperature chart).
Rest: Remove the roast from the oven and let roast rest covered with foil for 30 minutes before slicing. Cut the bones away from the roast if using bone-in, then slice the meat against the grain into ½- to 1-inch slices. Serve with au jus and horseradish sauce.
Notes
How to make au jusPour off most of the fat from the roasting pan, leaving the browned bits behind. Set the pan over medium heat, add a splash of broth, and scrape up everything stuck to the bottom. Add 2 cups beef broth, a sprig of rosemary and a smashed garlic clove, and simmer for 10 minutes until slightly reduced. Strain, season with salt and pepper, and keep warm.