In a large 8-quart stockpot, dissolve the salt in the hot water. Add the rest of the brine ingredients and stir to combine. Let cool to room temperature. Add the ice cubes to the brine.
Rinse the turkey breast under cold water and then place it in the brine. Add enough cold water to totally cover the turkey breast by at least ½ inch. Carefully stir the brine again. Cover and refrigerate for about 12 hours.
Remove the turkey breast from the stockpot and discard the brine. Pat dry with paper towels.
Place a large foil pan on top of the Flavorizer bars, below the cooking grate. Fill it halfway with room temperature water. Prepare the grill for cooking over medium heat (400°F).
Place the turkey, skin side up, in a roasting rack set inside a large disposable foil pan. Brush the skin with the melted butter. Grill the turkey breast above foil pan, over medium heat, with the lid closed, until the skin is golden and the internal temperature reaches 165°F in the thickest part of the breast (not touching the bone), about 1½ hours. Remove from the grill and let rest for 15 minutes (the internal temperature will rise a few degrees during this time). Cut into thin slices.