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1
Make the rub: add all the rub ingredients to a small bowl; stir to mix; set aside 1 1/2 tablespoons of the rub for the Lexington Vinegar Sauce.
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2
Sprinkle remaining rub all over the pork, patting it onto the meat with your fingers.
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3
Set up grill for indirect grilling; for gas grill, place all of the wood chips in the smoker box; run the grill on high until you see smoke, then decrease heat to medium-low.
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4
When ready to cook, place the pork, skin side up, in the center of the hot grate, over the drip pan and away from the heat; cover the grill.
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5
Cook the pork until darkly browned on the outside and very tender inside, 4-6 hours (instant read thermometer should read 195u00b0; if the pork starts to brown too much (and it probably will), cover it loosely with foil, but remember that those browned bits are good, too.
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6
Make the sauce: add sauce ingredients plus 1 1/2 tablespoon reserved rub to a large nonreactive bowl along with 1/2 cup water.
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7
Whisk until the sugar and salt dissolve; store in refrigerator until ready to use; bring to room temperature before using.
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8
Make the slaw: Remove core from the cabbage and discard.
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9
Cut cabbage into 8 chunks; finely chop cabbage in a food processor using the metal blade and pulsing the motor; work in several batches so you don't overcrowd the processor bowl.
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10
Transfer cabbage to a large bowl; stir in 2 1/2 cups Lexington Vinegar Sauce; taste for seasoning, adding more vinegar sauce as necessary; can be made up to 4 hours ahead; store in the refrigerator covered.
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11
When pork is done, transfer to a cutting board, cover it loosely with foil; let rest for 20 minutes.
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12
Then pull the pork into large pieces, discarding any bones or lumps of fat.
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13
Using a fork, pull each piece of pork into thin shreds; transfer pulled pork to a large foil pan and stir in 1 to 1 1/2 cups vinegar sauce-enough to keep the meat moist.
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14
To serve: mound the pulled pork onto hamburger buns; top with coleslaw and let everyone add more vinegar sauce to taste.
