Combine ⅓ cup (packed) darkish brown sugar, ⅓ cup Diamond Crystal or ¼ cup Morton kosher salt, 2 Tbsp. chili powder, 2 Tbsp. smoked paprika, 1 Tbsp. freshly floor black pepper, 1 Tbsp. garlic powder, 1 Tbsp. floor coriander, and 1 Tbsp. onion powder in a medium bowl to mix. Place one 12–14-lb. turkey, neck and giblets eliminated, patted dry, breast facet up, on a wire rack set inside a big rimmed baking sheet. (If you happen to don’t have this setup, place turkey on a V-shaped rack set inside a big roasting pan.) Sprinkle dry brine throughout inside and outside of turkey, patting to stick and nudging some into crevices. Chill hen, uncovered, a minimum of 12 hours and as much as 2 days.
Let turkey sit at room temperature 1 hour earlier than cooking.
Stack two 16×12″ items of professional quality foil on a floor and mound 2 cups wooden chips on high. Convey lengthy sides of foil collectively and fold up tightly to seal; fold brief sides beneath to create a pouch. (Folding the perimeters beneath will create further layers of safety from the warmth.) Repeat course of with extra foil and remaining wooden chips to make 2 extra pouches. Utilizing a paring knife, poke about 15 holes in high of every pouch.
If utilizing a fuel grill: Put together grill for medium-low oblique warmth (set one burner to medium-high warmth; go away remaining burners off). Place a wood-chip pouch straight over flame; place a drip tray on cooler facet of grill. Cowl grill and warmth to 300° (place an oven thermometer within the middle of oblique facet of grill if there isn’t one inbuilt). Flippantly oil grate.
If utilizing a charcoal grill: Fill chimney starter with charcoal; gentle and let burn till coals are lined with a skinny layer of ash. Pour out coals and financial institution to cowl one third of grill. Place a wood-chip pouch straight on high of coals; set a drip tray on cooler facet of grill. Place grate on grill, cowl, and warmth to 300°, adjusting vents on high and backside of grill as wanted to regulate temperature (place an oven thermometer within the middle of oblique facet of grill if there isn’t one inbuilt). Flippantly oil grate.
If utilizing a smoker: Put together smoker and warmth to 300° in line with producer’s instructions. Flippantly oil grate.
In the meantime, place 1 medium pink onion, quartered, inside turkey cavity. Utilizing your fingers, gently separate pores and skin from breast meat beginning at neck. Work 4 Tbsp. unsalted butter, room temperature, beneath pores and skin, spreading evenly over each breasts. Tie legs along with kitchen twine and tuck wings beneath.
Place turkey, breast facet up, over oblique warmth and canopy grill. Grill turkey, basting with melted butter (from remaining ¾ cup (1½ sticks) unsalted butter, melted) each half-hour, rotating hen 180° each hour, and changing wood-chip pouch every time smoke dissipates, till pores and skin is golden brown and an instant-read meat thermometer inserted into the thickest a part of turkey breasts registers 145°, 3¼–3¾ hours. Keep watch over the temperature contained in the grill and purpose to keep up warmth at 300° as a lot as doable. If utilizing a charcoal grill, gentle a chimney of coals and add as wanted.
Rotate turkey so breast is as removed from direct warmth as doable and proceed to grill, nonetheless lined, till pores and skin is deeply browned and an instant-read meat thermometer inserted into the thickest a part of the thighs registers an inside temperature of 165° (breast ought to register 155°), 30–60 minutes longer.
Switch turkey to a chopping board and let relaxation a minimum of half-hour and as much as 1 hour earlier than carving.