Remove the prime rib from the refrigerator 2 to 3 hours before cooking to come to near room temperature. Pat the roast dry on all sides with paper towels.

Preheat oven

Preheat oven to 225°F (107°C) for a low-and-slow roast that yields even doneness from edge to center.

Season

In a small bowl combine kosher salt, freshly ground black pepper, minced garlic, chopped rosemary and olive oil. Rub the mixture evenly all over the roast, pressing so it adheres. Place roast bone-side down (fat cap up) on a rack in a roasting pan. If bones are frenched, rest roast on bones so fat is exposed to heat.

Slow Roast

Insert an oven-safe probe thermometer into the center of the thickest part of the roast, avoiding bone. Roast at 225°F (107°C) until internal temperature reaches 115°F (46°C) for rare or 125°F (52°C) for medium-rare; for a 6 lb roast expect 3 to 4 hours depending on oven and shape. Check temperature after 2.5 hours, then every 20–30 minutes.

High-Heat Sear (Reverse Sear)

Increase oven temperature to 500°F (260°C) or set to broil. Transfer roast (keep juices in pan) and roast for 8–12 minutes, or until exterior is deep brown and crusty and internal temp reaches 125°F (52°C) for rare/130–135°F (55–57°C) for medium-rare. Watch closely to avoid burning.

Rest and slice

Remove roast from oven, transfer to a cutting board, tent loosely with foil and rest 20–30 minutes (carryover will raise temp a few degrees). Slice between the ribs into individual ribs or slice across for boneless-style portions. Reserve pan juices for au jus.

Horseradish Cream

While the roast rests, stir together prepared horseradish, sour cream, mayonnaise, lemon juice, Dijon mustard, salt and pepper in a small bowl. Taste and adjust horseradish (add more if you want more heat) and seasoning. Chill until ready to serve. The sauce pairs best served chilled or at room temperature alongside the warm sliced beef.

Au Jus

While roast rests and after you have removed roast from roasting pan, place the roasting pan over medium heat on the stovetop (or transfer pan juices to a medium saucepan). Add the chopped shallot and sauté in the pan drippings for 1–2 minutes until soft.

Pour in the red wine (or 1 cup additional beef stock) to deglaze the pan, scraping browned bits from the bottom with a wooden spoon. Reduce until slightly thickened, about 2–3 minutes.

Add 1 cup beef stock and the reserved strained pan drippings (aim for about 1 to 1 1/2 cups total liquid). Add thyme sprig. Simmer gently 5–8 minutes to meld flavors. Skim fat if desired.

Remove thyme sprig. Swirl in 1 tablespoon unsalted butter off heat to give the jus a glossy finish. Season with 1/2 teaspoon salt and 1/4 teaspoon freshly ground black pepper, taste and adjust. Keep warm and serve alongside sliced prime rib, spooning a small amount over each portion or serving in a small pitcher.