Combine paprika and next 6 ingredients (through dry mustard); reserve 1 tablespoon paprika mixture. Rub half of remaining paprika mixture onto pork. Place in a large zip-top plastic bag; seal and refrigerate overnight.
Remove pork from refrigerator; let stand at room temperature 30 minutes. Rub remaining half of paprika mixture onto pork.
Combine reserved 1 tablespoon paprika mixture, 1/3 cup vinegar, Worcestershire, oil, and beer in a small saucepan; cook over low heat 5 minutes or until warm.
Remove grill rack; set aside. Prepare grill for indirect grilling, heating one side to medium-low and leaving one side with no heat. Maintain temperature at 225°. Pierce bottom of a disposable aluminum foil pan several times with the tip of a knife. Place pan on heated side of grill; add half of wood chunks to pan. Place another disposable aluminum foil pan (do not pierce pan) on unheated side of grill. Pour 2 cups water in pan. Coat grill rack with cooking spray; place grill rack on grill.
Place pork on grill rack over foil pan on unheated side. Close lid; cook 4 1/2 hours or until a thermometer registers 170°, gently brushing pork with beer mixture every hour (avoid brushing off sugar mixture). Add additional wood chunks halfway during cooking time. Discard any remaining beer mixture.
Preheat oven to 250°.
Remove pork from grill. Wrap pork in several layers of aluminum foil, and place in a baking pan. Bake at 250° for 2 hours or until a thermometer registers 195°. Remove from oven. Let stand, still wrapped, 1 hour or until pork easily pulls apart. Unwrap pork; trim and discard fat. Shred pork with 2 forks.
While pork bakes, prepare slaw. Combine onion and next 5 ingredients (through 1/4 teaspoon salt) in a large bowl. Add cabbage, and toss to coat. Cover and chill 3 hours before serving. Serve pork and slaw on buns with Memphis Barbecue Sauce.
With so many great sauces, this recipe will go with any great sauce that delivers the kick you like for great BBQ.
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