Special equipment: 6 cups hickory wood chips soaked in water for 30 minutes, then drained; small aluminum tray
Place the pork butt on a rimmed sheet tray. Whisk together the brown sugar, dry mustard, salt, paprika, chili powder, garlic powder, black pepper, cayenne and celery seed together in a small bowl to blend. Rub the mixture all over the pork butt. Cover with plastic wrap and let marinate for at least 1 hour at room temperature or up to overnight in the fridge. Let come to room temperature for 1 hour before smoking.
Fill a small aluminum tray with the drained wood chips. Place the tray under the far left grill grates. Heat your grill to medium-high heat and heat for 20 minutes. The chips should start to ignite and smoke. Turn the far right burner off after 20 minutes.
Place the pork fat-side up on the far right on the grill grates over the unlit burner. Cover the grill and cook until tender and a fork can easily twist in the meat with no resistance, about 7 1/2 hours, maintaining a temperature of 275 to 300 degrees F. The internal temperature should reach 190 degrees F. You will need to add a handful of chips to the tray every few hours.
Remove the pork from the grill to a baking sheet and let rest for 30 minutes. Shred with forks and season the meat lightly with salt. Serve on soft white buns and topped with Sweet and Tangy Vinegar Slaw.
Whisk together the apple cider vinegar, canola oil, mayonnaise, mustard, sugar and celery seeds in a large bowl. Add the carrots, cabbage and shallots and toss all together. Top with salt and pepper. Cover with plastic wrap and refrigerate for at least 1 hour so the cabbage softens and the flavors all marry together.