Step 1: In a small bowl, mix the first 5 ingredients (Dijon mustard - black pepper). Smear this mixture evenly all over the prime rib. Place in a bowl or tray and cover with plastic wrap; refrigerate overnight.
Step 2: Once it has marinated, remove from the refrigerator and let come to room temperature.
Step 3: Preheat oven to 450-degrees F.
Step 4: Place the roast on a roasting pan, either on a rack or not. You can also make your own natural rack by placing whole celery, carrots, halved onions if you want the additional flavor to your gravy. Insert a meat thermometer into the roast, making sure it reaches the middle-center of the roast. This is super important and well worth the investment. I would never go without it.
Step 5: Place roast into the 450-degree F oven and roast 20 minutes. Reduce temperature to 200-degrees and roast 25 minutes per pound for rare, 30 minutes per pound for medium-rare, and 35 minutes per pound for medium to the desired temperature in the center of the roast according to the following reading per thermometer reading: 125-degrees-F (rare), 130-degrees-F (medium-rare), 135-degrees-F (medium). Forget about cooking it to a higher temperature to making it well-done, because it will defeat the purpose of a tender prime rib.
Step 6: Make sure that the bottom of the roasting pan is not drying out especially if you are planning on making Au Jus Gravy. Add a bit of beef stock to the bottom of the pan which will intermingle with the drippings to result in a gravy. Be though careful to not add way too much so as not to result in a “wet” prime rib because you want some toasty edges.
Step 7: Remove roast from the oven and carefully place it on a platter or roast cutting board. Tent it loosely with foil. Allow it to rest 15-30 minutes.
Step 8: If making au jus, place the roasting pan on the stove burners over medium-high heat. Add 2 1/2 - 3 cups beef stock (refer to Note). If you used a natural rack of vegetables, swirl the stock around with veggies to exude and release flavors, scraping up any and all brown bits. Taste for seasoning and adjust with salt and pepper, if necessary. Remove veggies (if used). Strain the sauce through a sieve to remove the solids before serving. De-grease, if necessary.
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