Combine the hot water and salt in a 54-quart cooler. Stir until the salt dissolves. Stir in the vegetable broth and the honey. Add the ice and stir. Place the turkey in the brine, breast side up, and cover with cooler lid. Brine overnight, up to 12 hours.
Remove the turkey from the brine and dry thoroughly. Rub the bird thoroughly with the vegetable oil.
Heat the grill to 400ºF.
Using a double layer of heavy-duty aluminum foil, build a smoke bomb: Place a cup of hickory wood chips in the center of the foil and gather up the edges, making a small pouch with an opening at the top. Set this directly on the charcoal or on the metal bar over the gas flame. Set the turkey over indirect heat, insert a probe thermometer into the thickest part of the breast meat, and set the alarm for 160ºF. Close the lid and cook for 1 hour.
After 1 hour, check the bird; if the skin is golden brown, cover with aluminum foil and continue cooking. Replace wood chips with second cup.
Once the internal temperature of the bird reaches 160ºF, remove from grill, cover with aluminum foil, and allow to rest for 1 hour. Carve and serve.