Instructions

Dissolve salt in 2 gallons cold water in large stockpot or clean bucket. Add turkey and refrigerate 4 to 6 hours.
Meanwhile, toast coriander, cumin, allspice, mustard, and cloves in small skillet over medium heat, shaking pan occasionally, until fragrant and wisps of smoke appear, 3 to 5 minutes. Cool mixture to room temperature, then grind to fine powder in dedicated coffee grinder or spice grinder or with mortar and pestle. Transfer mixture to small bowl, stir in paprika, ginger, thyme, cayenne, cardomom, cinnamon, and nutmeg; cover with plastic wrap, and set aside.
Remove turkey from brine and rinse under cool running water. Pat dry inside and out with paper towels. Place turkey breast-side up on flat wire rack set over rimmed baking sheet or roasting pan and refrigerate, uncovered, 30 minutes. Meanwhile, mix 1-tablespoon spice rub with vegetable oil and set aside. Remove turkey from refrigerator and wipe away any water collected in baking sheet; set turkey on baking sheet. Carefully separate skin from breast meat and rub oil/spice rub mixture directly onto breast meat. Rub 3 tablespoons spice rub inside turkey cavity. Apply remaining spice rub to turkey, beginning with back-side up and finishing with breast-side up, pressing and patting to make spices adhere, and picking up and reapplying any spice rub that falls onto baking sheet. Tuck wings behind back and tie ends of drumsticks together with twine. Set turkey on wire rack, set wire rack on baking sheet, and refrigerate, uncovered, 6 to 24 hours.
Ignite about 6 quarts (1 large chimney or about 6 pounds) charcoal briquettes and burn until covered with thin coating of light gray ash, about 15 minutes. Meanwhile, place 3 cups mesquite or hickory wood chips in center of 18-inch square heavy-duty aluminum foil; fold in sides to make a packet, then turn packet over and use fork to tear about 6 large holes in packet. Empty coals into grill and pile to one half of grill, creating a triple layer of briquettes. Place wood chip packet on coals, position grill grate over coals, and open bottom vents halfway. Spray V-rack with nonstick cooking spray and set turkey breast-side down on V-rack; set V-rack with turkey over cool side of grill. Open grill lid vent halfway and cover, positioning vent over turkey; grill-roast 1 hour.
Remove grill lid. Working quickly and using potholders, transfer V-rack with turkey to rimmed baking sheet. Remove grill grate; using tongs, move wood chip packet aside and add 12 new briquettes to coals. Replace wood chip packet and grill grate. Using large wads paper toweling, rotate turkey breast-side up and return V-rack with turkey to grill so that leg and wing that were facing coals are now facing away. Cover and continue grill-roasting until instant-read thermometer inserted into thickest part of thigh registers 170 to 175 degrees, 1 to 1 1/4 hours longer. Remove turkey from grill, let rest 20 to 30 minutes; carve and serve.