Take the prime rib out of the refrigerator 2-3 hours before cooking, place it on a cutting board, and pat the entire surface completely dry with paper towels. Let it sit uncovered at room temperature so the exterior dries slightly for better browning.
In a small bowl, combine the minced garlic, rosemary, thyme, olive oil, and Dijon mustard with the kosher salt, black pepper, onion powder, and smoked paprika. Mix into a thick paste and adjust seasonings to taste.
With the fat cap facing up, rub the herb mixture all over every surface of the roast, including the sides and bottom, pressing it in so it adheres. Season between the bones and meat if bone-in, then let the seasoned roast sit at room temperature for 30-60 minutes.
Place the roasting rack inside the roasting pan and position the prime rib on it with the fat side up and bones facing down. Make sure the roast sits securely and isn't wobbly.
Preheat the oven to 250°F (120°C). Once at temperature, place the roasting pan on the center rack and set a timer for 2 hours, avoiding opening the oven door frequently to prevent temperature fluctuations.
After about 1.5 hours, insert a meat thermometer into the thickest part of the roast, avoiding fat and bone. Remove at 115-120°F (46-49°C) for medium-rare or 125-130°F (52-54°C) for medium, accounting for carryover cooking.
Remove the roast from the oven and tent it loosely with aluminum foil. Let it rest for 20-30 minutes while you increase the oven temperature, so the juices redistribute throughout the meat.
Increase the oven temperature to 500°F (260°C), remove the foil, and return the roast to the oven. Roast for 6-10 minutes until the exterior is deeply browned and crusty, watching carefully to prevent burning.
Remove the roast from the oven, tent with foil again, and rest for 10 minutes. Remove the bones by running a knife along where they attach, then slice against the grain into 3/4-inch thick portions and serve immediately on a warm platter.