Light your grill and set it up for two-zone cooking. Add wood chunks (not chips) to the hot coals and establish temperature at 225° F as indicated with a reliable leave-in thermometer.
While your grill is preheating, add all the ingredients for the rub into a shaker bottle and shake to mix. Then evenly coat the roast with a very thin coat of neutral oil before seasoning the entire roast liberally with the rub.
Place the meat on the grill over indirect heat, close the lid, and allow it to smoke until the internal temperature reaches 175° F. Then increase grill temperature to 300° F and allow the pork to continue cooking until it reaches 190° F before removing it from the grill.
Allow the pork to rest for 10-15 minutes.
Slice in 1/4-inch thick slices for service, and lightly dust with a sprinkle of rub.