In a small bowl, combine rosemary, thyme, garlic, paprika, cayenne, white pepper, and oil.
Season the prime rib roast with salt and pepper, then generously rub with herb mixture. Wrap tightly with plastic wrap. Let it marinate overnight in the fridge for best results (up to 24 hours).
Remove the marinated roast from the fridge about 2 hours before cooking to allow it to come to room temperature.
Line the roasting pan with foil if desired, then add onions and celery.
Position the rack in the lowest part of the oven and heat to 450°F (230℃). Roast the prime rib for 30-45 minutes, then reduce the temperature to 325°F (160℃) and continue roasting until it reaches the desired internal temperature. An instant-read meat thermometer guarantees the roast turns out exactly how you want it. For an accurate reading, push the thermometer into the center of the roast, making sure the tip isn't touching fat or bone.
Check on the roast every 30-45 minutes and add about ½ cup water or stock as needed to prevent the pan from burning.
Also, cover the roast with foil if it browns too fast to prevent it from burning.
Gently transfer the roast to a large platter, then loosely cover it with foil and let it rest for 20-30 minutes before serving so the juices settle back into the meat.
Meanwhile, if making au jus, skim the fat from the drippings, leaving 2-3 tablespoons of fat.
Add stock, stir, and scrape the bottom of the pan to release any browned bits in the pan.
Transfer the drippings to a skillet, add red wine (if desired) and beef stock.
Bring to a boil and cook until the mixture is slightly reduced, 5-7 minutes. The sauce shouldn’t be thick; it’s a very light sauce—season with salt and pepper to taste.
Serve roast with au jus.