Prepare the pork butt: 1 hour before grilling, use a brush to cover pork butt in ½ cup of mustard and season with Carolina Dry Rub Brewery BBQ Seasoning.
Prepare the grill: Heat grill or smoker to 250 degrees. Cook pork butt, fat side up, until internal temperature reaches 160 degrees.
Remove pork from heat and double wrap with aluminum foil. Return to grill and cook until internal temperature reaches 204 degrees.
Remove meat and let rest, wrapped, for 1 hour.
Assemble the sandwiches: Working by hand or with a hand-mixer, shred the pork within a large bowl or deep sheet pan. Incorporate Gentry's BBQ Tenne-Sweet Memphis BBQ Sauce, mixing to fully coat the meat. Set aside.
Preheat oven to 250 degrees. Slice rolls horizontally and toast until lightly browned, about 8 to 10 minutes.
While buns toast, prepare the slaw. Combine shredded cabbage with mayonnaise, vinegar, 1 ½ tablespoons mustard, lime juice, salt, and pepper, and mix until creamy.
To serve, layer pork, slaw, and pickles over the bottom half of toasted rolls. Cover with top half and cut into individual servings.
