Poke 8 to 10 slits in an 8-pound bone-in pork shoulder; stuff with garlic cloves. Whisk 1/4 cup each paprika and brown sugar, 2 tablespoons each kosher salt and black pepper and 1 teaspoon cayenne pepper. Rub all over the pork; refrigerate overnight. Preheat a grill to medium-high on one side. If using a gas grill, place 5 cups soaked wood chips in the smoker box. For a charcoal grill, toss 1 cup wood chips onto the hot coals; add more hot coals and chips every hour. Place the pork, skin-side up, in an aluminum pan with 1 1/2 cups water on the cooler side of the grate. Cover and cook, rotating every hour, until the meat reaches 180 degrees, 5 to 6 hours. Mix 1 cup cider vinegar, 1/2 cup water, 1/3 cup ketchup, 3 tablespoons sugar and 1 tablespoon each Worcestershire sauce, salt and pepper; brush onto the pork every 20 minutes until it reaches 200 degrees, 1 to 2 more hours (keep the grill covered). Let rest 15 minutes. Remove the skin, shred the meat and toss with more vinegar sauce. Serve on rolls.
Photograph by Tina Rupp
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