Though the turkey goes with any favorite Thanksgiving accompaniments, for a holiday diversion, I suggest you replace gravy with a classic, robust red chile adobo sauce to drizzle on and jícama-cranberry relish to give the perfect counterpoint. For wine: a reserva tempranillo from Rioja, Spain, is perfect.
- Brining the turkey. If the turkey has a metal clamp on its legs, remove it. Place two large food-safe plastic bags (we like Reynolds turkey roasting bags) in a large, clean, deep dishpan or plastic bucket. Add 1 gallon of the water, the sugar, salt and pepper flakes. Stir the mixture to dissolve the sugar and salt. Add the remaining gallon of water and mix. Place the turkey in the mixture breast side down making sure it is completely covered in brine. Squeeze the air out of the bag and tie it shut. Refrigerate 12 hours or overnight.
- Setting up the grill for indirect cooking. Soak 2 cups of mesquite chips in water to cover for at least 30 minutes. Heat a gas grill to medium-high or light a charcoal fire and let it burn just until the coals are covered with gray ash and very hot. When the grill is ready, either turn the burner(s) in the center to medium-low or bank the coals to the sides for indirect cooking. Add some of the soaked wood chips to the grill (for a gas grill, place them in a smoker attachment box or wrap the chips in foil; for charcoal, place them on the hot coals). For the charcoal grill, set the grill grate in place.
- Preparing the turkey for the grill. Remove the turkey from the brine and pat thoroughly dry with paper towel. (If you are not cooking the turkey at this point, place it in the outer baking bag, which should be dry and clean, and store it in the refrigerator. Discard the brine.) Rub the inside of the turkey cavity with the crushed garlic. Stuff the herbs and bay leaves inside, then tie the legs together with a cotton string. Pull the skin over the neck opening and secure with a small skewer. Set the turkey on a roasting rack set inside a heavy-gauge foil pan. Brush turkey lightly with oil.
- Grilling the turkey. Set the turkey in the pan on the cooking grate. Pour 1 cup water around the pan. Cover the grill and cook over medium heat. To maintain an even temperature with a charcoal grill, add more charcoal regularly (usually a few pieces every half hour or so). Keep adding wood chips as desired to give smokiness.Check the turkey periodically, you may want to cover the wing tips and/or the whole turkey to prevent the skin from getting too brown. The turkey is done when its juices run clear and the internal temperature of the thickest part of the thigh is about 155 degrees. Estimate about 12 to 14 minutes per pound, typically 2 1/2 to 3 hours.
- Serving the turkey. Remove the turkey from the grill, cover loosely with foil and let stand 15 minutes. (The temperature will rise 5 to 10 degrees as the turkey rests.) Carve the turkey, arrange on a warm platter and serve with the warm Red Chile Adobo Sauce and the Jícama-Cranberry Relish.