Simmer 1 quart of the apple cider with the spice for about 10 minutes to infuse the cider with the spice aromatics. Stir in salt to dissolve. Combine the infused cider with the remaining quarts of apple cider.
Pour the brine solution into your brining container. Do not place bird directly into hot cider. Add additional cold water so the overall temp of the solution approaches room temp. Place bird in container and add enough additional water to cover the bird.
If time allows, brine the bird overnight in a refrigerator.
Remove the bird from the brine. Discard the liquid. Place the bird in a roasting rack and return to the refrigerator. Allow to dry overnight, uncovered, in your refrigerator. If an exposed bird makes you a little nervous, cover with a very loose piece of foil.
8 to 12 hours in brine. Overnight to dry. If you need to lean toward one side of the brining equation, allow more time for skin to dry. Slightly dry skin will help to promote a golden brown, crispy texture.
Remove your brined bird from the refrigerator. Give it about 45 minutes resting at room temperature to allow the temperature of the bird to elevate a bit.
Pat dry your brined turkey. Rub the room-temperature butter all over the bird. Sprinkle the bird with salt and pepper. Place apple, orange, onion and sage in the cavity. Tie legs with kitchen twine.
Make sure you have a full bag of charcoal.
Place an appropriately sized disposable aluminum pan in the bottom of a charcoal grill; add a few cups of water. Fill a charcoal chimney with charcoal and light.
We’ll be using the grill like an oven. Cook with the indirect method: When coals are covered with ash, spread half on either side of disposable pan. Set top grate on grill.
Place turkey on grate over pan (do not allow any part of turkey to sit over coals). Cover grill. Insert stem of an instant-read thermometer into hole in grill hood. Maintain temperature as close as possible to 350° by opening vents to increase temperature and closing vents to reduce it, lifting grate with turkey to replenish coals as needed using charcoal chimney. If using wood chips, scatter a handful of drained chips over charcoal every 30 minutes. The more chips, the greater the smoked flavor.
Make sure your gas tank is full.
Light all burners and set the temperature to medium high. After 10 minutes, turn off the center burner. We’ll be cooking with the indirect method.
Place turkey on the grate over the unlit burner. Close lid. Adjust temperature so the grill maintains 350°. If using a smoker box, add soaked chips to the box.
Cook turkey, rotating every hour for even browning (lift the grate with the turkey on it; rotate grate 180 degrees), until an instant-read thermometer inserted into thickest part of the thigh without touching bone registers 160° (juices should run clear when thermometer is removed), estimate approximately 15 minutes per pound. But, check the temperature every 15 minutes after about an hour and a half.
Keep an eye on the skin covering the breast. If the skin starts to look too brown, cover with a piece of aluminum foil.
When the temperature reaches 160°, remove from grill and transfer turkey to a platter. Tent with foil and let rest for 1 hour before carving.