Smoked Paprika Dry-Rubbed Pulled Pork Sandwiches

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Pulled Pork: 

3 tablespoons smoked paprika

2 tablespoons coarsely ground black pepper

2 tablespoons coarse salt

1 tablespoon chili powder

1 tablespoon garlic powder

1 tablespoon brown sugar

One 5- to 7-pound Boston pork butt

Two 12-ounce bottles wheat ale beer

1 cup store-bought barbeque sauce

Coleslaw:

1 1/4 cups mayonnaise

1/3 cup rice wine vinegar

2 teaspoons granulated sugar

2 1/2 pounds green cabbage, cored and finely shredded

1 large carrot, coarsely grated

Kosher salt and freshly ground black pepper

12 brioche buns, split