Make small holes all over the pork shoulder with a thin sharp knife and stuff in garlic cloves. Rub the meat all over with the Memphis Shake; cover and refrigerate overnight.
Prepare an outdoor grill with an indirect medium-hot fire with a mix of briquettes and hardwood charcoal in half of the grill. Set grate over coals. Place pork, skin side up, in an aluminum pan with about 1 1/2 cups water on the cooler side of the grate. Toss 1 cup of the soaked and drained wood chips onto the coals and cover the grill, making sure the lid's vents are directly over pork.
When the coals cool to medium-low heat, preheat a chimney-full of hot briquettes and hardwood charcoal. Whenever smoke stops coming out of the vents, about every hour, add more hot coals and 1 cup of soaked and drained wood chips to the fire. The goal is to maintain a medium-heat, smoky fire (but don't worry if it is hotter when the coals are added and cooler while preheating the coals). Rotate the pork when you add coals so it cooks evenly. Cook the meat until an instant-read thermometer inserted into the thickest part of the pork registers 180 degrees F, about 6 hours.
Set aside 1 quart of the North Carolina-Style Vinegar BBQ Sauce. Once the pork reaches 180 degrees F, begin mopping the entire surface of the meat every 20 minutes with some of the remaining sauce and the pan drippings. Continue to cook the pork, covering the grill between mopping, until an instant-read thermometer registers 200 degrees F, about 1 to 2 hours more.
Transfer the pork to a cutting board and let rest for at least 15 minutes. Remove the outer skin and discard. Cut large chunks from the bone and shred, using 2 forks or your fingers, (when cool enough to touch) or chop. Toss with about 1 cup of the reserved barbecue sauce for every 3 cups of meat. Tuck the pork into the soft rolls and serve with pickles.
Whisk paprika, brown sugar, oregano, garlic, ancho powder, salt, and celery salt in a small bowl. Store in an airtight container in a cool, dry place for up to 2 months.
Heat the vinegar and sugar in a medium saucepan over medium heat until the sugar dissolves. Off the heat, stir in the ketchup, honey, salt, red pepper, and black pepper.
Toss the extra sauce with shredded cabbage, or you can serve it on the side for those who want more spice. Use leftover pork for nachos. Ancho powder is simply finely ground dried ancho chiles. Anchos are the sweetest of the dried chiles and are not terribly hot, so don't be put off by the amount used in this recipe. BBQ experts assert that the vinegary North Carolina sauces are the original American sauces. Within the state, you know which side of the Piedmonts you are on by what sauce douses your pulled pork. Along the coast, sauces are reduced to the basics-vinegar and red pepper. Up in the mountains, tomato makes an appearance, and the sauces are thicker.
From Food Network Kitchens Get Grilling, Meredith, 2005