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For the Dry Rub:
Add all the dry rub ingredients into a medium-sized bowl and stir until thoroughly combined.
For the pork shoulder:
Place the pork, fat side up, on a clean baking sheet. Season the pork on all sides with salt and pepper then rub the dry rub all over the pork, pressing into the meat. Cover the pork with plastic wrap and place into the refrigerator for 7 hours.
Black Pepper Vinegar Sauce:
Place all the ingredients into a blender and blend until emulsified. Add water if the sauce is too thick.
Green Onion Slaw:
Place the green onions, vinegar, chiles, mayonnaise, salt, pepper and oil into a blender and blend until emulsified. Place the cabbage and red onions in a bowl, add the dressing and stir until combined. Fold in the cilantro and season with salt and pepper, to taste.
For the pork shoulder:
Remove the pork from the refrigerator 30 minutes prior to cooking.
Following manufacturer's instructions and using lump charcoal and 1/2 cup drained wood chips for a smoker, or 1 cup for a barbecue, start fire and bring temperature of smoker or barbecue to 225 degrees F to 250 degrees F. Place the pork on the rack in smoker or barbecue. Cover and cook until an instant-read thermometer inserted into the center of the pork reaches 165 degrees F. Turn pork every 45 minutes, about 6 hours total. If using the smoker, after 2 hours place the pork into the smoker pan and fill halfway with chicken stock. (This is to prevent the shoulder from drying out.)
Add more charcoal, as needed, to maintain 225 degrees F to 250 degrees F and more wood drained wood chips (1/2 cup for the smoker or 1 cup for the barbecue with each addition) to maintain smoke level.
Transfer pork to a clean rimmed baking sheet. Let stand until cool enough to handle. Shred into bite-size pieces. Mound on platter and toss with most of the Black Pepper Vinegar Sauce, reserving the rest for drizzling the bun. Pour any juice from the baking sheet over the pork.
Chef's Note: This can be made 1 day ahead. Transfer the pork and any juices to a baking dish. Cover with foil and chill. Before continuing, re-warm pork, covered, in a 350 degrees F oven for about 30 minutes.
Drizzle the sauce on the top and bottom of the bun. Top the bottom bun with the meat, another drizzle of sauce, Green Onion Slaw and finish with the top of the bun.