In a medium saucepan over medium-high heat on the stove, bring the apple cider to a boil and boil until reduced to 180 milliliters, 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 to 30 minutes before grilling.
Prepare the grill for indirect cooking over medium heat (180° to 230°C).
Prepare the grill for cooking over medium heat (200°C).
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, 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 and let rest until cool enough to handle, about 10 minutes. Toast the buns, cut side down, over direct heat, with the lid closed, for about 1 minute.
Brush the cooking grates clean. Grill the chicken legs over medium heat, with the lid closed, 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 and let rest until cool enough to handle, about 10 minutes. Toast the buns, cut side down, over direct 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 return to the stove over medium heat; cook 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.
