This is truly the anti-vegetarian dish. Prime rib is one of those classics you can pull out that will always blow people away. It's a good special occasion dish, so good that the occasion may be nothing at all. When ordering the rib roast from a butcher, be sure to request a "top choice" roast cut from the small loin end, the best being ribs 12 through 10. Have the butcher cut off the chine (backbone) to make carving easier. The rib bones look best if they are shortened and frenched (the butcher will be happy to do this for you as well, unless he's a sourpuss, in which case get a new butcher).
Preheat the oven to 350 degrees F. Lay the beef in a large roasting pan with the bone side down. (The ribs act as a natural roasting rack.)
In a small bowl mash together the garlic, horseradish, rosemary, thyme, salt, pepper, and olive oil to make a paste. Massage the paste generously over the entire roast. Scatter the vegetables around the meat and drizzle them with a 2-count of oil. Put the pan in the oven and roast the beef for about 1 1/2 to 2 hours for medium-rare (or approximately 20 minutes per pound). Check the internal temperature of the roast in several places with an instant-read thermometer; it should register 125 degrees F. for medium-rare. Remove the beef to a carving board and let it rest for 20 minutes. The internal temperature of the meat will continue to rise by about 10 degrees. Remove the vegetables and set aside. Pour the pan juices into a fat separator or small bowl and set aside to allow the fat and beef juices to separate. Pour off and discard the fat. You can use the tasty beef juices for Sauteed Mushrooms.