Preheat the oven to 400 degrees . In a large bowl, toss the coleslaw mix with 1/2 tsp. salt; set aside.
On a foil-lined baking sheet, season the chicken with salt and pepper. Bake, turning once, for 40 minutes.
In a dutch oven, combine 1 cup vinegar, 3 tbsp. brown sugar, the ketchup, crushed pepper, allspice and 1/4 tsp. each salt and pepper. Boil for 5 minutes.
Using 2 forks, shred the meat and skin from the chicken bones; add to the sauce and stir in 1/4 cup water. Cook to blend the flavors, about 5 minutes.
In a bowl, whisk the remaining 1 tbsp. brown sugar with the remaining 2 tbsp. vinegar; drizzle onto the slaw. Stir in the EVOO; toss to coat.
Divide the chicken among the rolls; top with some slaw. Serve with the chips and extra slaw on the side