In a small saucepan
, bring 1 cup water to a boil. Stir the salt and brown sugar into the boiling water until dissolved. Place the ice cubes in a large container. Pour the brine
over the ice cubes and stir to mix and cool. Add the leg quarters to the cooled brine, adding additional water if needed to make sure they are submerged. Refrigerate overnight.
Remove the chicken from the brine, rinse and pat dry. Preheat the grill to medium-high. Turn one side of the grill off and place the chicken
skin-side down over the indirect heat. Cook for 10 minutes, turn, cook another 10 minutes and then brush with a thick coating of basting sauce. Turn, cook another 10 minutes, baste
and cook a final 10 minutes for a total of 40 minutes on the grill
. The chicken should register at least 160 degrees F and the juices should run clear. Serve immediately.