Trim the pork shoulder by cutting away any larger chunks of fat and trimming the fat cap down to about ¼ inch.
Lightly rub the shoulder all over with the mustard, and season generously with the rub. For best results, place the shoulder in a pan and refrigerate, covered with plastic wrap, for 12–24 hours.
Preheat the grill to 250°F. Preheat for at least 15 minutes and brush the grill grates clean.
Add the shoulder to the grill, fat cap up, and cook until the bark has set (the rub is not pasty or rub off on your finger) and the internal temperature is around 165°F, 6–8 hours.
Remove the shoulder from the grill and wrap in a double-layer of aluminum foil, being sure not to crimp the foil too tightly.
Return the shoulder to the grill and continue cooking until a probe slides through the meat with little resistance and the internal temperature is around 200°F, 2–4 hours more.
Remove the shoulder from the grill, wrap in a towel, and transfer to a cooler to rest until the internal temperature is 140°–150°F, 4–6 hours.
Pull the shoulder into bite-sized pieces and mix in some of the drippings from the aluminum foil package.
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