First: Combine all the dry ingredients in a glass or stainless steel bowl. Trim the excess fat from the butt. After cleaning and drying the meat, rub a light coat of the yellow mustard onto the meat. This will help the rub stick to the meat and does not create any mustard flavor. Next, sprinkle or rub the spice mixture onto the pork shoulder on all sides. You may now place the butt on the grill or refrigerate it for 3 to 6 hours for more flavor by cover it with plastic wrap and placing it in the refrigerator.
Next: When you are ready to begin cooking, fire up the grill for indirect grilling and place a drip pan under where the butt will reside. This will catch the fat which will be rendered in cooking. You might consider taking the meat out of the refrigerator several hours early so the meat can come close to room temperature.
Next: If you will be using a gas grill, take some wood chips which have been soaked in apple juice (or water) and place in the smoker box. Place the smoker box into your preheat the grill and when smoke appears, reduce the heat to medium.
Next: If you will be using a charcoal grill, preheat the grill to medium-low around 250°F.
Next: Place the pork shoulder on the hot grate over your drip pan. Hold your 250°F for about an hour and then reduce to 225°F for the duration of the cooking process.Close the grill and allow the pork shoulder to cook the until the bone can be easily twisted and come free from the meat. The internal temperature on an instant-read meat thermometer should reache 190°F, and hold that temperature for at least 1 hour. Please allow plenty of time to cook the meat. As the meat reaches maximum temperatures, the rise in cooking temperatures slows down drastically. The temp and size of the piece of meat will determine the cooking time.
Next: Carefully pull the meat from the bone and then pull the pork into pieces. Using forks or Bear Paws, shred the meat into 1 to 2 inches long and 1/8 to 1/4 inch wide strips. Place the shredded pork in a pan. From there, you can add vinegar sauce or barbecue sauce (to keep it moist) or even additional dry rub seasoning to add more flavor. Cover with aluminum foil to keep warm.