Pulled Pork Barbecue

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Dry Rub:

3 tablespoons paprika

1 tablespoon garlic powder

1 tablespoon brown sugar

1 tablespoon dry mustard

3 tablespoons coarse sea salt

1 (5 to 7 pound) pork roast, preferably shoulder or Boston butt

Cider-Vinegar Barbecue Sauce:

1 1/2 cups cider vinegar

1 cup yellow or brown mustard

1/2 cup ketchup

1/3 cup packed brown sugar

2 garlic cloves, smashed

1 teaspoon kosher salt

1 teaspoon cayenne

1/2 teaspoon freshly ground black pepper

Pan drippings from the pork

12 hamburger buns

1 recipe Cole Slaw, recipe follows

Pickle spears, for serving

Cole Slaw:

1 head green cabbage, shredded

2 carrots, grated

1 red onion, thinly sliced

2 green onions (white and green parts), chopped

1 fresh red chile, sliced

1 1/2 cups mayonnaise

1/4 cup Dijon mustard

1 tablespoon cider vinegar

1 lemon, juiced

Pinch sugar

1/2 teaspoon celery seed

Several dashes hot sauce

Kosher salt and freshly ground black pepper