Remove the prime rib from the refrigerator 1 hour before cooking. Pat dry with paper towels. Rub olive oil over the roast, then evenly coat with kosher salt, black pepper and garlic powder. Let sit on a rack at room temperature for 45–60 minutes.

Roast and rest

Preheat oven to 450°F (230°C). Place the roast on a rack set in a roasting pan, fat side up. Roast at 450°F for 15 minutes to develop a crust, then reduce oven temperature to 325°F (160°C) and continue roasting until internal temperature reaches 125°F (52°C) for medium-rare (about 12–15 minutes per pound from the reduced-temp stage). Use an instant-read thermometer in the thickest part. Remove roast and tent loosely with foil; rest 20–25 minutes (temperature will rise roughly 5–10°F during resting).

Thinly slice

After resting, transfer roast to a cutting board. Using a sharp slicing knife, carve very thin slices (about 1/16–1/8 inch). If you prefer, partially freeze the roast for 20–30 minutes to make slicing thinner, then cut against the grain for tender slices. Keep slices warm on a tray covered loosely with foil.

Au Jus / Pan Sauce

Deglaze the roasting pan

Place the roasting pan over two burners on medium heat (or transfer drippings to a skillet). Add the red wine (if using) and scrape up browned bits with a wooden spoon. Let simmer 1–2 minutes until wine reduces slightly.

Make the sauce

Pour in beef stock and add Worcestershire sauce. Bring to a gentle simmer and reduce for 6–8 minutes until slightly concentrated. In a small bowl, whisk the butter and flour into a smooth paste (beurre manié) and whisk into the simmering jus to slightly thicken. Simmer 1–2 more minutes. Season with 1/2 tsp salt and 1/4 tsp pepper, taste and adjust. Strain through a fine sieve into a small saucepan and keep warm on low.

Caramelized Onions

Cook onions slowly

Heat a large skillet over medium-low heat. Add 1 tablespoon butter and 1 teaspoon olive oil. Add the thinly sliced onions, sprinkle with 1 teaspoon brown sugar, 1/4 tsp salt and a pinch of black pepper. Cook, stirring occasionally, 25–35 minutes until onions are deep golden brown and sweet. If onions begin to stick, add 1–2 tablespoons water and continue cooking. Remove from heat and keep warm.

Sliders & Assembly

Toast buns

Preheat broiler or skillet. Brush insides of slider rolls with melted butter. Place cut-side up on a sheet pan and broil or toast in skillet until lightly golden, about 1–2 minutes under the broiler—watch closely to avoid burning.

Warm prime rib slices

If the slices cooled while slicing, warm them briefly: heat a skillet over medium-low, add a splash (1 tsp) of beef jus or butter, and quickly warm slices 30–45 seconds per side until just warmed through. Keep slices covered and warm.

Assemble sliders

Spread a thin layer of horseradish sauce on the bottom halves of the toasted rolls (if using). Pile 2–3 thin slices of prime rib per slider, top with 1–2 tablespoons caramelized onions and a small pinch of arugula if desired. Spoon a teaspoon of warm au jus into a small dipping bowl per serving or, for a saucier slider, lightly brush a little jus onto the meat before topping and place top bun on slider. Finish with a light sprinkle of coarse sea salt.

Serve

Arrange sliders on a platter with au jus for dipping. Serve immediately so buns stay warm and onions retain texture. Leftover au jus keeps 2–3 days refrigerated.