For the brine
8 cups apple cider 1 lb. kosher salt (1-3/4 cups if using Morton’s; 2-3/4 cups if using Diamond Crystal) 1-3/4 cups packed dark brown sugar 1 cup apple cider vinegar 3/4 cup honey 1/4 tsp. ground cloves 5 dried bay leaves 1 12- to 14-lb. turkey (preferably fresh, and not kosher or self-basting; neck and giblets, excluding liver, reserved for the broth) For the broth
1/4 cup vegetable oil Kosher salt 2 medium carrots, cut into 2-inch chunks 2 medium celery stalks, cut into 2-inch chunks 1 medium yellow onion, peeled and quartered 1 dried bay leaf 1/2 tsp. black peppercorns For the barbecue spice rub
1/4 cup granulated sugar 2 Tbs. chili powder 1 Tbs. packed dark brown sugar 2-1/4 tsp. smoked paprika (pimentón) 1-1/2 tsp. kosher salt 3/4 tsp. freshly ground black pepper 1/2 tsp. cayenne 1/2 tsp. garlic powder 1/2 tsp. onion powder 1/2 tsp. dry mustard 1/8 tsp. ground cinnamon 1/8 tsp. ground coriander 1/8 tsp. ground cumin For the turkey
5 Tbs. vegetable oil 1 medium yellow onion, peeled and quartered 4 oz. (1/2 cup) unsalted butter, softened, plus 2 oz. (4 Tbs.), cut into 4 slices 1/4 cup honey about 2 lb. thick-cut bacon, preferably applewood smoked, at room temperature 2 cups hardwood chips, preferably a combination of apple and hickory, soaked in water for at least 30 minutes and drained 1 cup apple juice, in a spray bottle For the gravy
1-1/2 oz. (6 Tbs.) unbleached all-purpose flour 1/2 tsp. cider vinegar, or to taste Kosher salt and freshly ground black pepper
Make the brine
Combine all of the brine ingredients and 8 cups of water in an 8-quart pot; bring to a boil over high heat, stirring occasionally. Remove from the heat, cool to room temperature, and then refrigerate until cold.
Brine the turkey
Put the turkey breast side down in a pot or tub large enough to hold it and the brine. Add the brine (the turkey will float, but that’s OK) and refrigerate for at least 6 hours and up to 20 hours.
Make the broth
With a chef’s knife, cut the turkey neck into 3 or 4 pieces and chop the giblets. Heat the oil in a 4-quart pot over medium-high heat. Cook the neck and giblets with a pinch of salt, stirring often, until browned, about 8 minutes. add the carrots, celery, onion, bay leaf, peppercorns, 2 tsp. salt, and 6 cups of water.
Bring to a boil, lower the heat, skim off any foam, and simmer, covered, until flavorful, about 1 hour. Strain the broth through a fine sieve into a large bowl—you’ll have about 4 cups.
Make the spice rub
In a small bowl, mix all of the rub ingredients, breaking up any clumps of brown sugar with your fingers.
Prepare the grill
Light a charcoal or gas grill fire and set it up for indirect cooking over low heat (275°F).
If using a charcoal grill, bank the lit and ashed-over coals to one side of the grill. Cover the grill and adjust the vents as needed to reach 275°F.
If using a gas grill, cover the grill, turn off one or more of the burners, and adjust the active burner(s) to reach 275°F.
Smoke the turkey
Rinse and dry the turkey; discard the brine. Rub the inside of the body and neck cavities with 2 Tbs. of the vegetable oil, and then sprinkle each cavity with 1/2 Tbs. of the spice rub. Put the onion pieces inside the body cavity.
In a small bowl, combine the 4 oz. softened butter with 1 Tbs. of the spice rub. Carefully slide your hands under the skin of the turkey to loosen it from the breast. Using your fingers, spread the butter mixture directly on the breast meat, being careful not to tear the skin.
Tie the legs together with twine. Tuck the wing tips behind the neck, securing any loose skin over the neck cavity beneath them.
Rub the outside of the turkey with the remaining 3 Tbs. vegetable oil, then the honey, and then 3-1/2 Tbs. of the spice rub.
Put a flat wire rack inside an 11x14-inch (or similar) foil-lined roasting pan. Line the rack with enough bacon slices (touching but not overlapping) to cover the area the turkey will occupy. Put the turkey breast side up on the bacon and then lay enough bacon slices across the top of turkey to cover it, securing the slices with toothpicks. (It’s OK if the sides of the turkey aren’t entirely covered.)
For a charcoal grill, sprinkle 1/2 cup of the drained wood chips over the coals. Replace the grill grate.
For a gas grill, make 2 heavy-duty aluminum foil packets, each filled with 1 cup of the drained chips. Using a fork, poke holes all over the packets. Lifting the grill grate, set one of the packets directly over an active burner; reserve the second packet. Replace the grill grate.
Put the turkey in its pan on the unlit side of the grill and cover the grill. Smoke the turkey until the bacon is dark, rotating the pan occasionally for even cooking, 2 to 3 hours. If using a charcoal grill, add 1/2 cup of drained chips to the coals every 30 minutes until you’ve used all of the chips. When the temperature dips to 250°F, every 1 to 1-1/2 hours, light 3 quarts of charcoal in a chimney set over bricks. When the coals are ashed over, transfer the turkey in its pan to a heatproof surface, lift the grill grate, and add the fresh coals to maintain the temperature. If the temperature gets too high, leave the lid ajar to let in cool air. For a gas grill, add the reserved packet of chips when the first packet stops smoking.
When the bacon is dark, remove it from the top of the turkey; enjoy as a cook’s treat or discard. Generously season the turkey with all but 1 tsp. (which will be used for the gravy) of the remaining spice rub. Put the butter slices on top of the breast and thighs and continue smoking, spraying the turkey with the apple juice and rotating the pan every 30 minutes, until the temperature in the center of the breast registers 165°F, about 2 hours more. If at any time the turkey becomes too dark, loosely tent it with foil.
Remove the pan from the grill. Tilt the turkey so the juice in the cavity runs into the roasting pan. Transfer the turkey to a serving platter or cutting board and loosely tent it with foil. Let the turkey rest for at least 30 minutes.
Make the gravy
Heat the turkey broth until hot. Pour the drippings from the roasting pan into a fat separator or heatproof measuring cup. Allow the fat to rise to the top and then transfer 1/4 cup of the fat to a 12-inch skillet; discard the remaining fat and reserve the rest of the drippings.
Season the turkey broth with enough of the drippings to add flavor without making it too salty.
Heat the fat in the skillet over medium heat. Whisk in the flour and cook, whisking constantly, for 2 minutes. Add the remaining 1 tsp. spice rub and cook, whisking, 1 minute more. Gradually whisk the broth into the skillet until smooth, and then bring to a simmer. Whisk in the cider vinegar and simmer until the gravy barely coats the back of a spoon, about 5 minutes. Season to taste with salt and pepper.
Carve the turkey and serve with the gravy.
Make Ahead Tips
The spice rub can be made up to 1 month ahead; keep in an airtight container.
The broth can be made up to 2 days ahead; refrigerate when cool.
The turkey can be brined 2 days ahead, then removed from the brine, patted dry, and refrigerated for up to 1 day, covered with plastic wrap.