Preparation Combine all ingredients in heavy large saucepan. Bring to boil over medium heat, stirring occasionally. Reduce heat to medium-low; simmer uncovered until sauce thickens and flavors blend, stirring frequently, about 15 minutes. (Can be made 1 week ahead. Cover; chill.)
For the rub 1 tablespoon mild paprika 2 teaspoons light brown sugar 1 1/2 teaspoons hot paprika 1/2 teaspoon celery salt 1/2 teaspoon garlic salt 1/2 teaspoon dry mustard 1/2 teaspoon freshly ground black pepper 1/2 teaspoon onion powder 1/4 teaspoon salt
For the barbecue 1 Boston butt (bone-in pork shoulder roast; 5 to 6 pounds), covered with a thick (1/2 inch) layer of fat
Preparation 1. If using the rub, combine the mild paprika, brown sugar, hot paprika, celery salt, garlic salt, dry mustard, pepper, onion powder, and salt in a bowl. Wearing rubber or plastic gloves if desired, rub the spice mixture onto the pork shoulder on all sides, then cover it with plastic wrap and refrigerate it for at least 3 hours, preferably 8. If not using the rub, generously season the pork all over with coarse (kosher or sea) salt and freshly ground black pepper; you can start cooking immediately.
2. Set up the grill for indirect grilling and place a drip pan in the center. If using a gas grill, place all of the wood chips in the smoker box and preheat the grill to high; when smoke appears, reduce the heat to medium. If using a charcoal grill, preheat the grill to medium-low and adjust the vents to obtain a temperature of 300°F.
3. When ready to cook, if using charcoal, toss 1 cup of the wood chips on the coals. Place the pork shoulder, fat side up, on the hot grate over the drip pan. Cover the grill and smoke cook the pork shoulder until fall-off-the-bone tender and the internal temperature on an instant-read meat thermometer reaches 195°F, 4 to 6 hours (the cooking time will depend on the size of the pork roast and the heat of the grill). If using charcoal, you'll need to add 10 to 12 fresh coals to each side every hour and toss more wood chips on the fresh coals; add about 1/2 cup per side every time you replenish the coals. With gas, all you need to do is be sure that you start with a full tank of gas. If the pork begins to brown too much, drape a piece of aluminum foil loosely over it or lower the heat.
4. Transfer the pork roast to a cutting board, loosely tent it with aluminum foil, and let rest for 15 minutes.
5. Wearing heavy-duty rubber gloves if desired pull off and discard any skin from the meat, then pull the pork into pieces, discarding any bones or fat. Using your fingertips or a fork, pull each piece of pork into shreds 1 to 2 inches long and 1/8 to 1/4 inch wide. This requires time and patience, but a human touch is needed to achieve the perfect texture. If patience isn't one of your virtues, you can finely chop the pork with a cleaver (many respected North Carolina barbecue joints serve chopped 'cue). Transfer the shredded pork to a non reactive roasting pan. Stir in 1 to 1 1/2 cups of the vinegar sauce, enough to keep the pork moist, then cover the pan with aluminum foil and place it on the grill for up to 30 minutes to keep warm.
6. To serve, mound the pulled pork on the hamburger buns and top with coleslaw.
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