1 pint apple cider or apple juice
½ cup ketchup
2 tablespoons plus 1 teaspoon cider vinegar
1 tablespoon packed light brown sugar
½ teaspoon granulated garlic
¼ teaspoon dry mustard
⅛ teaspoon ground cinnamon
2 teaspoons paprika
1 teaspoon granulated garlic
½ teaspoon kosher salt
¼ teaspoon chipotle chile powder
2 tablespoons extra-virgin olive oil
4 whole chicken legs, each 10 to 12 ounces, skin removed
4 cups shredded coleslaw blend
⅓ cup mayonnaise
2 tablespoons apple cider or apple juice
2 tablespoons cider vinegar
1 teaspoon granulated sugar
¼ teaspoon freshly ground black pepper
6 hamburger buns, split
Bread-and-butter pickle chips (optional)
In a medium saucepan over medium-high heat, bring the apple cider to a boil and boil until it has reduced to ¾ cup, 10 to 12 minutes. Stir in the remaining sauce ingredients and return to a simmer. Reduce the heat to medium and continue simmering the sauce until it is slightly thickened, 8 to 10 minutes, stirring occasionally. Remove the saucepan from the heat and set aside.
In a small bowl combine the rub ingredients. Stir in the oil to make a wet rub. Brush the chicken legs evenly on both sides with the wet rub. Allow the chicken legs to stand at room temperature for 20 minutes before grilling.
Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F). Meanwhile, in a medium bowl combine the slaw ingredients and mix well. Set aside.
Brush the cooking grates clean. Grill the chicken legs over indirect medium heat, with the lid closed as much as possible, until the juices run clear and the meat is no longer pink at the bone, 50 minutes to 1 hour, turning once. Remove the chicken legs from the grill, transfer to a rimmed baking sheet, and let rest until cool enough to handle, about 10 minutes. Toast the buns, cut side down, over direct medium heat, with the lid closed, for about 1 minute.
Using two forks or your fingers, pull the chicken apart into shreds. Add the chicken to the saucepan with the sauce and heat over medium heat until hot, 2 to 3 minutes. Pile the chicken on the buns and top with coleslaw. Serve with bread-and-butter pickle chips, if desired.