Combine brine ingredients in a large bowl. Add chicken to mixture, cover, and place into the refrigerator for 2 hours. Remove from bowl, discard brine and rinse off wings. Blot dry with paper towels and place onto a parchment-lined baking sheet. Use two if needed.
Preheat grill for medium-high heat or oven for 350 degrees F. Combine rub and season wings. Place onto the grill or in oven for 40 minutes, or until the wings register and an internal temperature of 175 degrees F. Reduce heat on the grill if flare-ups occur, or simply move to a cooler part of the grill and cook over indirect heat until done.
While wings are cooking, bring sauce ingredients to a light simmer over medium-high heat. Stir, reduce heat and let the sauce simmer over low for about 4-5 minutes.
Once wings are cooked, place into a large clean bowl. Pour warm sauce over top and using a sturdy pair of tongs, toss to coat. Serve immediately with a side of chunky blue cheese dressing.