Mix sugar, paprika, mustard, cumin, garlic powder, onion powder, cayenne, salt, and pepper together. Place ingredients in large plastic zip-lock bag. Dump chicken wings or drumsticks into bag and shake until all chicken is coated; transfer to slow cooker. Pour 1/2 cup of the barbecue sauce over chicken and stir to coat. Cover and cook until chicken is tender, 3-4 hours on low for wings, 4-6 hours on low for drumsticks.
Position oven rack 10 inches from broiler element and heat on high. Place a wire cooling rack on an aluminum foil-lined rimmed baking sheet and coat the wire rack with vegetable oil spray. Transfer chicken to prepared baking sheet; discard braising liquid that remains in slow cooker.
Brush chicken with 1/2 cup more barbecue sauce and broil until lightly charred and crisp (to your liking), about 10 to 15 minutes. Flip chicken over, brush with remaining 1/2 cup barbecue sauce, and continue to broil until lightly charred and crisp on second side, 5 to 10 minutes longer. Serve.
Note about drumsticks... I've made these with wings and drumsticks and the wings do turn out much more juicy and have more flavor. Drumsticks are good, but we all prefer the wings.