In a large 8-quart stockpot, dissolve the salt in the 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 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.
Prepare the grill for indirect cooking over medium heat (350° to 450°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 over indirect medium heat, with the lid closed, until the skin is golden and the internal temperature reaches 160° to 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 5 to 10 degrees during this time). Cut into thin slices.