Make the dry rub

1. Stir together all dry rub ingredients in a bowl; set aside.

Make the vinegar-cayenne mopping sauce

1. Whisk together all vinegar-cayenne mopping sauce ingredients in a large bowl; set aside.

Smoke the turkey

1. Pat turkey dry with paper towels and place turkey, breast side up, on a large cutting board. Using a chef’s knife, carefully cut turkey breast in half lengthwise, cutting straight through breastbone. Open up turkey and press to flatten; pat inside dry with paper towels. Sprinkling from about 12 inches above work surface, coat turkey on all sides with dry rub; do not rub in seasoning. Place turkey, skin side up, on a rimmed baking sheet. Let stand at room temperature while grill preheats, up to 2 hours.

2. Prepare a charcoal fire in a grill or smoker according to manufacturer’s instructions. Place oak wood chunks on coals and fit grill with an aluminum foil–lined diffuser, such as convEGGtor. Maintain internal temperature at 225°F for 15 to 20 minutes. Smoke turkey, skin side up, covered with lid, until meat around ends of drumsticks pulls back and reveals the turkey’s “socks” and a thermometer inserted in thickest part of breast registers 145°F, about 2 hours.

3. Generously mop 1 1/2 cups mopping sauce on skin side of turkey. Using long tongs and reaching as far under the bird as possible, carefully flip turkey skin side down. (Underside of turkey should be dark mahogany brown and evenly speckled with charred bits.) Generously mop with remaining 2 1/2 cups sauce. When sauce begins to pool in cavity, insert tip of tongs into exposed breast meat and gently twist to allow sauce to soak into meat. Continue to mop until all the sauce is absorbed. Close grill and smoke until skin side is lightly charred and a thermometer inserted in thickest part of breast registers 155°F, 30 to 45 minutes. Transfer turkey to a large cutting board; carve immediately, or let rest up to 2 hours.