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1
Preheat grill to 325 degrees, building fire on opposite sides of grill if using charcoal, or on one side or opposite sides if using gas.
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2
Season pork with rub.
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3
If using charcoal, every hour for first 4 hours add fresh coals and toss 1/2 cup wood chips on each mound of coals.
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4
If using gas, place wood chips in smoker box, and preheat until you see smoke (depending on model of gas grill, use all 4 cups at once or 1 cup every hour for first 4 hours).
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5
Place pork, fat side up, on grill over drip pan, away from fire.
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6
Barbecue until nicely browned and cooked through, for 4 to 6 hours, or until internal temperature is 195 degrees, so that the meat will shred properly.
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7
Meanwhile, combine ingredients for vinegar sauce in a bowl with 3/4 cup water, and whisk to mix.
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8
Add additional salt or sugar to taste, if desired.
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9
Transfer cooked pork to cutting board, cover with foil, and let it rest until cool enough to handle, about 15 minutes.
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10
Pull meat into pieces, and discard any skin, bones or fat.
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11
With fingertips or a fork, pull each piece of pork into shreds about 2 inches long and 1/4 inch wide.
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12
(Or finely chop the meat with a cleaver.)
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13
Transfer to metal or foil pan, and stir in 1 cup vinegar sauce, or enough to keep meat moist and flavorful.
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14
Cover with foil, and place on grill to keep warm until serving.
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15
Serve on hamburger buns with cole slaw and remaining sauce on side.
