Remove the pork shoulder from its packaging and pat if dry.
Trim the fat cap if it's too thick, leaving 1/4". Score it in a checkered pattern.
Coat the entire pork shoulder with mustard and season with an all purpose rub.
Set up the grill for indirect heat at 250 degrees. Place the seasoned pork directly on the grates.
After the first 4 hours on the grill, spritz the pork every hour with Apple cider vinegar.
Continue cooking until the internal temperature of the pork reaches 170-175 degrees.
Transfer the pork shoulder from the grill and place it in an aluminum pan or on a large foil sheet. Add brown sugar, honey, cubed butter and sweet BBQ seasoning.
Wrap the pan tightly with aluminum foil and place it back on the grill. Increase the grill temperature to 275 degrees Fahrenheit.
Continue to cook until the internal temp of the pork shoulder reaches around 200 degrees.
Check for probe tenderness. If it doesn't go in smoothly, place it back on the grill and continue cooking.
Remove the wrapped pork from the grill and let it rest for 1 hour in an oven or insulated cooler.
Remove the bone and shred the meat, mixing it in with all the rendered juices.
Notes
Try to purchase a bone-in pork shoulder. Helps cook more evenly.
If you are not a fan of mustard in general, use hot sauce or Worcestershire sauce as the binding agent.
For the first 4 hours, leave the pork should on the grill. Do NOT peek inside. Let the grill do its magic. After that, you should start to check the bark and see it is not drying out.
At this stage of the cook, no more smoke will penetrate the meat. It's OK to finish the cook in the oven.
Tenderness is key. This will help make the pork shreddable. The final temperature on a classic pulled pork can range anywhere from 200 to 205 degrees, so be patient. If the probe is not going into the meat smoothly, it's not done. Keep cooking. This is where a lot of the mistakes are made. Pork is removed too soon and the meat ends up dry and tough.