Prime Rib is a Marketing Term used in Restaurants. The meaningful name is Beef Rib Roast or Standing Rib Roast when it is on the Bone and usually labeled Boneless Rib Eye or just Rib Eye when trimmed up. I would leave the Fat, give it a good rub down with Montreal Steak Seasoning or other Rub you like and Smoke it at 225* to 250*F figuring 30 to 40 minutes per pound to 120*F IT for Rare, 130*F for Med/Rare, 140*F for Medium, 150*F for Med/Well and 160*F for Worthless. Give the meat a Rest on the counter tented with foil of at least 30 minutes or in a cooler wrapped in foil for up to 2-3 hours. I highly recommend making some Smokey Au Jus. Here is the Recipe. Have fun...JJ
Smokey Au Jus
1- Lg Onion,
4-5 Carrots,
3-4 Ribs Celery
3-4 Peeled Cloves of Garlic
Toss them in a pan under the Beef, and let the whole deal Smoke for one hour,
THEN add 4-6 Cups Beef Broth,
2 Tbs Tomato Paste,
1/2tsp Dry Thyme (4-5 sprigs Fresh)
1-2 ea Bayleaf
Finish the Smoking process to the IT you want.
While the Roast is resting, dump the pan juices veggies and all into a 2-3Qt Sauce pot and add 1Cup Red Wine, something you like to drink, and bring the Jus to a boil, lower the heat and simmer 20-30 minutes. Strain out the veggies and let the Jus rest a minute or so for the Fat to rise. Skim off the bulk of the fat then using strips of paper towel laid on top of the Jus then quickly removed, take off the last little bit of fat.
The purpose of Smoking the Vegetable for 1 hour before adding the Broth and Herbs is...The Smoked vegetables Roast in the Dry heat concentrating their Flavors and Sweetness giving the finished Jus a Richer, Deeper, Full Flavor.
Serve the sliced Beef Au Jus or thicken the Jus to make Gravy.
NOTE: If you are using this recipe with Brisket, additional Water will have to be added periodically to maintain the proper volume. Do not add more Broth as repeated addition and reduction will make the Au Jus too salty..