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1
Mix together the Neelys barbecue rub, pepper, and salt.
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2
Rinse the shoulder or butt thoroughly, pat dry with paper towels, and massage the seasoning mixture into the meat.
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3
Cover the meat with plastic wrap, and refrigerate for at least 2 hours, or up to 1 day in advance.
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4
Following the manufacturers instructions, and, using lump charcoal and 1/2 cup of soaked and drained wood chips for the smoker (or 1 cup for the kettle grill), start a fire, and bring the temperature of the smoker or barbecue grill up to 275 degrees F.
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5
Place the pork on a rack in the smoker or on the grill.
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6
Cover, and cook the meat until a thermometer inserted into the center registers 165 degrees F, turning the pork every hour or so, about 6 hours total.
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7
Add more charcoal as needed to maintain the temperature, and more drained wood chips to maintain the smoke level.
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8
Transfer the pork to a rimmed baking sheet (this is importantyoull want to catch all the flavorful juices), and allow it to stand until cool enough to handle.
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9
Shred the pork into bite-sized pieces, and mound on a platter.
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10
Pour any juices from the baking sheet over the pork.
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11
At this point the pork can be served immediately, or covered with foil and refrigerated for a day.
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12
If you chill the pork, rewarm it, covered, in a 350-degree oven for about 30 minutes.
