Prepare either a charcoal or gas grill for indirect cooking.
Remove pork from wrapper. Do not trim off any excess fat — it will naturally baste the meat and keep it moist during the long cooking time. Brush pork with a thin coating of oil. Season with salt and pepper or barbecue rub. Set aside on a clean tray until ready to cook.
Before placing the meat on the grill, put the soaked wood chips directly on white-gray ash briquettes or in the smoking box of your gas grill. If using a charcoal grill, you will need to add charcoal every hour to maintain the heat. If using a pellet smoker, smoke at 220° F for 2 hours to get maximum smoke on the meat and then raise the temperature to between 280° F and 325° F to finish cooking and render the fat.
Place pork in the center of the cooking grate, fat side up. Cook slowly for 4 to 5 hours at between 325° F and 350° F or until an instant-read meat thermometer inserted into the middle of the pork registers 190° F to 200° F.
At this point, the meat should be very tender and falling apart. If there is a bone in the meat, it should come out smooth and clean, with no meat clinging to it. (This is the real test for doneness on the barbecue circuit.) Note: there is no need to rotate the meat during cooking. If using a mop (the term for both a brush for basting and a vinegar-based sauce used to keep meat moist), begin basting the pork after it has been cooking for 2 hours and continue to do so every 40 minutes until it is done.
Refrain from basting during the last 20 minutes of cooking time. This will ensure that the crust is dry, caramelized, and crisp when you remove the pork from the grill.
Let the meat rest for 20 minutes or until cool enough to handle. Wearing nitrile food-service gloves, pull meat from the skin, bones, and fat. Set aside any crispy bits (fat) that have been completely rendered and look almost burned. Working quickly, shred the chunks of meat with two forks by crossing the forks and “pulling" the meat into small pieces.
Chop the reserved crispy bits and mix into the pulled pork. While the meat is still warm, mix with enough barbecue sauce (see recipe) to moisten and season the meat, about ¾ cup.
To reheat: Place pork in a pan covered tightly with aluminum foil with about ¼ cup additional barbecue sauce in oven at 250° F; remove the pan from the oven and stir the pork occasionally. It will take about 40 to 60 minutes to reheat, depending on the quantity of pork. Once it's hot, stir well and re-season with a little more sauce.
Serve sandwich style on a hamburger bun and top with Lexington Coleslaw (recipe follows). Serve additional sauce on the side, if desired.
North Carolina Coleslaw