The pork shoulder here is fixed a bit more elaborately than what you’d find at your average South Carolina roadside barbecue joint—I’ve added a mustard rub and a mustard mop. Depending upon where you are in South Carolina, the pork will be pulled, chopped, or even sliced (my choice for this recipe).
Step 1: Make the rub. Place the mustard, paprika, salt, black pepper, white pepper, garlic powder, onion powder, and cayenne in a bowl and stir to mix. (Actually, if you don’t have sensitive skin, your fingers work better for mixing a rub than a spoon or whisk does.) Sprinkle the rub all over the pork, patting it onto the meat with your fingertips. Let the pork cure at room temperature while you make the mop sauce.
Step 2: Make the mop sauce. Combine the vinegar, mustard, salt, and black pepper in a large nonreactive mixing bowl, add 1/2 cup of water, and whisk until the salt dissolves.
Step 3: Set up the grill for indirect grilling and preheat to medium-low. If using a gas grill, place all of the wood chips or chunks in the smoker box or in a smoker pouch and run the grill on high until you see smoke, then reduce the heat to medium-low. If using a charcoal grill, place a large drip pan in the center, preheat the grill to medium-low, then toss 1 cup of the wood chips or chunks on the coals.
Step 4: When ready to cook, place the pork, skin side up, if there is one, in the center of the hot grate, over the drip pan and away from the heat, and cover the grill. Cook the pork until darkly browned on the outside and very tender inside, 4 to 6 hours. To test for doneness, use an instant-read meat thermometer: The internal temperature of the pork should be about 195°F. (Yes, this is very well-done—that’s how you get pork tender enough to chop or pull.) If the pork starts to brown too much (and it probably will), cover it loosely with aluminum foil, but remember that the browned bits are good, too. Every hour for the first 4 hours, swab the pork with some of the mop sauce, using a barbecue mop or basting brush. If using a charcoal grill, every hour you’ll need to add 12 fresh coals and 1/2 cup of wood chips or chunks to each side.
Step 5: Transfer the cooked pork to a cutting board, cover it loosely with aluminum foil, and let it rest for 20 minutes. You could pull or chop the pork, but I like to thinly slice it across the grain (the practice of many South Carolina pit masters). Place the pork slices in an aluminum foil pan. If you are not quite ready to serve, cover the pan with aluminum foil and place it on a warm—not hot—grill or in an oven turned on low to keep warm.
Step 6: f you’re feeling fancy, brush the hamburger buns with the melted butter and lightly toast them on the grill (work directly over the coals or a lit burner). Otherwise, skip the butter and simply serve the buns without toasting. Load each bun with sliced pork and slather with South Carolina Mustard Barbecue Sauce. Top the pork and sauce with pickle slices and serve at once.