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Click here to see how it's done.
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For the Dry Rub:
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Add all the dry rub ingredients into a medium-sized bowl and stir until thoroughly combined.
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For the pork shoulder:
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Place the pork, fat side up, on a clean baking sheet.
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Season the pork on all sides with salt and pepper then rub the dry rub all over the pork, pressing into the meat.
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Cover the pork with plastic wrap and place into the refrigerator for 7 hours.
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Black Pepper Vinegar Sauce:
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Place all the ingredients into a blender and blend until emulsified.
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Add water if the sauce is too thick.
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Green Onion Slaw:
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Place the green onions, vinegar, chiles, mayonnaise, salt, pepper and oil into a blender and blend until emulsified.
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Place the cabbage and red onions in a bowl, add the dressing and stir until combined.
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Fold in the cilantro and season with salt and pepper, to taste.
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For the pork shoulder:
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Remove the pork from the refrigerator 30 minutes prior to cooking.
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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.
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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.
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If using the smoker, after 2 hours place the pork into the smoker pan and fill halfway with chicken stock.
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(This is to prevent the shoulder from drying out.)
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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.
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Transfer pork to a clean rimmed baking sheet.
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Let stand until cool enough to handle.
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Shred into bite-size pieces.
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Mound on platter and toss with most of the Black Pepper Vinegar Sauce, reserving the rest for drizzling the bun.
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Pour any juice from the baking sheet over the pork.
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Chef's Note: This can be made 1 day ahead.
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Transfer the pork and any juices to a baking dish.
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Cover with foil and chill.
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Before continuing, re-warm pork, covered, in a 350 degrees F oven for about 30 minutes.
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For assembly:
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Drizzle the sauce on the top and bottom of the bun.
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Top the bottom bun with the meat, another drizzle of sauce, Green Onion Slaw and finish with the top of the bun.