This is a traditional American style smoked pulled pork, although the flavours change from region to region across the country this is a pretty generic version, perhaps leaning towards a Memphis style.
Trim the pork to remove any tags, residual bone shards and/or excessive fat.
Rub: Rub the piece of pork with mustard, sprinkle with the pork rub to create an even dark coverage. Let sit while to set the smoker and wait for it to come to temperature, about 1 hour.
Smoke: Place the pork on a smoker at 110 degrees C, that has a hickory or similar wood for smoke, about 3 to 5 chunks. Smoke for 3 hours.
Wrap: Prepare two large layers of foil that can wrap the pork. Place the pork on the top sheet of foil, then add the apple juice, honey, brown sugar, and butter. Wrap tightly. Then wrap a second time with the second piece of foil.
Return to the smoker and continue to cook for an additional 3 hours. After 3 hours, using a temperature probe check the temperature and resistance of the pork. The meat starts to reach its finished time at about 108 degrees C, however use the feeling of the pork to make the final decision, the softer it is the easier it will pull, the longer it cooks the softer it gets.
Glaze: Combine the BBQ sauce, apple juice, and apple cider vinegar. Unwrap the pork, using a basting brush, coat the pork with the BBQ sauce mixture then return to the smoker for 15 minutes to let the glaze set.
Rest the pork for 30 to 90 minutes before pulling. The remaining sauce can be stirred through the pulled pork.