STEEP tea bag in water in a large bowl for 5 minutes, covered. Remove tea bag and discard.
WHISK in sugar and salt until dissolved. Add ice, lime juice, lime halves, and mint; stir. Place the chicken in brine and refrigerate, covered, at least 2 hours.
BLEND all the dry spices for the rub together. Remove chicken from brine and massage both sides with the rub before grilling.
Place the chicken skin side down on the grill and set 2, which have been wrapped in heavy duty foil, on top of chicken. Cover and cook (over medium heat) until browned, 5 to 10 minutes. Flip the chicken over, replace the brick and grill 20 to 25 minutes more, or until the internal temperature reaches 155 degrees.
Glazing: Remove the bricks and glaze every 2 - 3 minutes until 16o degrees. Then take the bird off the grill and let it rest.