Set the smoker to 225°F, with lid closed. Let it preheat for 20 minutes. We recommend using apple wood pellets for this dish. They will impart a slightly sweeter smoke that goes great with the rub.
Combine dry rub ingredients in a bowl.
Trim excess fat from the pork shoulder, score fat with a sharp knife (only slice about 1/8" into pork), then cover it with the dry rub. Reserve some dry rub to be sprinkled on the meat after it has been shredded.
Place the pork onto the smoker.
Place the pork onto the smoker. Smoke the pork until the internal temperature reaches 203°F (about 10 hours). You can wrap it in butcher paper once it reaches 160°F if you want to speed up the cooking time (your final bark won't be as good though).
Once the pork reaches 203°F, remove it from the smoker then wrap it tightly in aluminum foil. Place wrapped pork into a cooler for 1 hour.
After 1 hour, remove the pork from the foil and pull out the bones, using 2 forks to shred the pork to your desired consistency.
Sprinkle leftover dry rub onto the pork and toss to coat.