Whisk together the apple juice, salt, brown sugar, and molasses in a large container (large enough to fit your bird) until the salt and sugar have dissolved.
Stir in the ice cold water and submerge the turkey, breast side down, into the brine. Refrigerate for 12 hours.
In a small bowl, combine all ingredients for the rub and mix well.
Remove the turkey from the brine and pat dry with paper towels.
Use your fingers to gently separate the skin from beneath the breasts and around the thighs. Mix softened butter about 1 1/2 tablespoons of the rub under the breast and thighs then sprinkle the remaining rub all over the turkey and inside of the cavity.
Preheat your grill or smoker to 325°F. Add your wood chunks when at temperature.
Place your turkey in a large roasting pan on a rack, breast side up add 2 cups of water to the bottom of the pan.
Smoke for 1 hour, then completely cover with aluminum foil and continue smoking until an internal temperature of 150°F is reached in the thickest part of the breast, around another 1-2 hours. Uncover and baste the bird every 15-20 minutes with the melted butter and continue smoking until the breast hits an internal temp of 165°F and 185°F for the legs.
Remove from the smoker and allow to rest, uncovered, for 20-30 minutes.
To get the skin extra crispy use a kitchen torch or put in an oven on broil for 3-5 minutes