Build a charcoal fire for indirect cooking by situating the coals on only one side of the grill, leaving the other side void. Add a small aluminum pan to the void side of the grill and fill it halfway with water.
In a small bowl, combine the dry rub ingredients. Coat the pork evenly with dry rub, patting gently until the mixture adheres to the meat.
When the grill reaches 250 degrees Fahrenheit, place pork butt on the void side of the grill over the water pan, close the lid, and cook over indirect heat for four hours.
While the pork is cooking, combine all of the baste ingredients in a medium saucepan and mix well. Place over medium-low heat and simmer until the butter melts. Keep baste on low heat until ready to use.
Cook pork an additional three hours basting the pork every hour until the internal temperature of the pork reaches 190 degrees Fahrenheit. Continually monitor the grill temperature and add hot charcoal as needed, to maintain the grill temperature of 250 degrees Fahrenheit.
Remove the pork butt from the charcoal grill and let it rest for 15 minutes. Pull the cooked meat from the bone and serve mounded high on slider buns topped with your favorite barbecue sauce.