Pat the butterflied turkey dry with paper towels. Liberally season all over with kosher salt and ground black pepper, making sure to get some seasoning under the skin where possible. Tuck the wing tips behind the back. Place the seasoned turkey on a wire rack set over a rimmed baking sheet and transfer to the refrigerator to dry brine, uncovered, for 8 to 24 hours. This helps develop flavor and crispy skin.

Light a full chimney of charcoal. Once all the charcoal is lit and coated in gray ash, pour it into the grill and arrange in a crescent moon shape on one side of the charcoal grate. Set the cooking grate in place, cover, and let the grill preheat for 5 minutes. Clean and oil the grilling grate. Place the wood chunk(s) directly on top of the hot coals to infuse the turkey with a subtle smoky flavor. I prefer using apple wood for a gentle, sweet smoke.

Remove the turkey on its rack from the baking sheet and transfer it to the grill, positioning legs and thighs closer to the hot coals and the breast over the cooler side. Cover the grill, placing the top vent over the cool side, and cook the turkey until an instant-read thermometer registers 165-170°F (74°C-77°C) in the thickest part of the thigh and 145-150°F (63°C-66°C) in the breast, about 90 minutes. Add more coals after an hour if needed to maintain heat.

Transfer the turkey (still on its rack) to a cutting board and let it rest at room temperature for 20 minutes to keep the juices inside. Remove the wire rack, carve the turkey, and arrange on a platter. Serve immediately with hot white wine and mustard gravy. I like to pour a little gravy over the carved meat right before serving for extra moisture and flavor.