Take the rib roast out of its packaging and place it bones down in a roasting pan. Sprinkle salt over all surfaces, cover lightly with plastic wrap, and allow it to reach room temperature for at least 2 hours.

Set the oven to 500°F (260°C). Use paper towels to dry the roast.

In a small bowl, mix the softened butter, olive oil, minced garlic, 1 tsp salt, pepper, thyme, and rosemary until thoroughly combined. Take off the plastic wrap and apply the mixture uniformly over the whole roast.

Place the prime rib in the preheated oven and roast for 15 minutes, then lower the oven temperature to 325°F (165°C) and keep roasting until the desired doneness. Use a meat thermometer to monitor the internal temperature: Rare: 120°F (50°C) (about 15–17 minutes per pound); Medium Rare: 130°F (55°C) (about 17–20 minutes per pound); Medium: 140°F (60°C) (about 20–23 minutes per pound); Medium Well: 150°F (65°C) (about 23–25 minutes per pound). Note: The beef will continue to cook as it rests out of the oven, so remove it from the oven 5–10 degrees before it reaches your optimal temperature.

Take the roast out of the oven and cover it loosely with foil. Let it rest for 30 minutes before carving.

Carve the prime rib roast by slicing against the grain into about ½-inch thick slices. Serve with au jus and horseradish, if desired.