BBQ Pulled Pork

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

1 1/2 cups cider vinegar

1 1/2 cups mayonnaise

1 cup yellow or brown mustard

1 head green cabbage, shredded

1 lemon, juiced

1 recipe Spicy Slaw, recipe follows

1 red chile, sliced

1 red onion, thinly sliced

1 tablespoon brown sugar

1 tablespoon cider vinegar

1 tablespoon dry mustard

1 tablespoon garlic powder

1 teaspoon cayenne

1 teaspoon salt

1/2 cup ketchup

1/2 teaspoon celery seed

1/2 teaspoon freshly ground black pepper

1/3 cup packed brown sugar

1/4 cup Creole mustard

12 hamburger buns

2 carrots, grated

2 garlic cloves, smashed

2 green onions, chopped

3 tablespoons coarse salt

3 tablespoons paprika

Pickle spears

Pinch sugar