Special equipment: a charcoal kettle-style grill; charcoal; 8 cups large smoking wood chips (applewood and hickory mix), soaked in water; butcher's twine
For the prime rib: Heat the charcoal until hot, then carefully arrange on one side of a kettle-style grill, and place the soaked wood chips over the hot coals. Place an aluminum pan filled with some water opposite to the coals to catch any drippings. Place a wire rack on the grill. Cover the grill to allow the smoke to accumulate and preheat to about 225 degrees F.
In a small bowl, add the granulated garlic, black pepper, salt, mustard powder, paprika and cayenne, and mix well. Rub the spice mixture all over the prime rib, then set aside. Combine the oregano, rosemary and thyme and tie together with butcher's twine. In a large cast-iron pan set over medium-high heat, add the oil. Rub the oil all over the pan using the herb bundle, then set aside. Place the prime rib fat-side down in the pan and sear until browned, 7 to 8 minutes. Flip over and sear the other side until browned, 4 to 5 minutes. Turn on its end and sear for 2 minutes.
Place the prime rib on the grill over the aluminum pan, with the thick end facing the coals. Place the lid on the grill. Smoke the prime rib until the internal temperature reaches 130 degrees F for medium-rare, 2 hours 30 minutes to 3 hours.
Remove the prime rib to a baking sheet and set aside to rest.
For the sauce: In a medium saute pan set over medium-high heat, add the garlic, parsley, black pepper, rosemary, thyme, salt, shallots and butter. Cook, stirring continuously, until the butter foams and the garlic turns a light golden color, 5 to 6 minutes. Add the broth, Worcestershire and demi-glace. Stir to combine, and cook until the sauce reduces by one-third, remove from the heat and set aside.
If the chine bone has been removed, slice the prime rib into generous 1-bone portions. Otherwise, slice off the bone and cut into generous portions, and then place on a platter. Spoon the sauce over the top, and serve.
This recipe can be made in an oven if you do not have a charcoal kettle-style grill. Skip the instructions for the charcoal and wood chips, and continue as directed.