Assemble all your ingredients before beginning to cook. Place the roast in a roasting pan, fat side up. Add water, stock, wine, or a combination to the bottom of the pan to about 1/3 to 1/2 inch in depth. Optional: Add a coarsely chopped medium onion, 2 to 3 chopped stalks of celery, and a handful of baby carrots in the bottom of the roasting pan and set the roast on top..
Heat about 1/2 cup olive oil in small saucepan. Add 3 to 4 bruised garlic cloves, salt, and pepper; mix well. Heat just until garlic starts to turn color.
Brush infused oil over roast. Let the roast rest to bring it up to room temperature—2 to 4 hours, depending on the roasts's size.
Preheat your oven to reach 450°F by the end of the roast's resting period.
Place the rib roast into the preheated oven and roast uncovered for about 10 minutes.
Reduce the oven temperature setting to 350°F, and continue roasting until you reach your desired degree of doneness. While the temperature accuracy of ovens can vary, you can estimate 12 to 13 minutes per pound of rib roast. But it’s always best to cook to an internal doneness temperature. (See step 8 below.)
Baste with pan drippings every 20 to 25 minutes. Be sure the pan does not roast dry. Add water, stock, or wine to keep the liquid replenished.
An instant-read thermometer is the key to a roast done to perfection. Don’t poke the roast too soon, or you’ll lose precious juices and flavor. Do your first check when about 80% of the estimated cooking time has elapsed, then you can adjust your final timing as necessary. Remove the roast from the oven when the internal temperature reaches within 5 degrees of your desired doneness. Final doneness temperatures are 130°F for rare, 140°F for medium-rare, or 150°F for medium.
Let the roast rest for 10 to 20 minutes, depending on its size. The roast’s internal temperature will continue to increase during the resting period by about 5 degrees to reach your desired doneness and the roast’s juices will have a chance to be reabsorbed throughout the beef. (Loosely tent the roast with aluminum foil, if desired.)