How to Make It
Preheat one side of grill to medium (375°F).
Combine first 6 ingredients. Remove giblets and neck from turkey; discard or reserve for another use. Place turkey, breast side down, on a cutting board. Using kitchen shears, cut along both sides of backbone; discard backbone. Turn turkey breast side up; press firmly against breastbone with the heel of your hand so that the bird is splayed open, butterfly style. Trim excess fat; tuck wing tips under turkey. Place turkey on a large rimmed baking sheet. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Rub spice mixture under loosened skin.
Coat grill grate with cooking spray. Place turkey, skin side up, on grate over unlit side of grill. Cover and grill 2 1/2 hours or until a thermometer inserted into thickest portion of thigh registers 160°F, rotating turkey 90 degrees every 30 minutes. Place turkey on a cutting board. Let stand, loosely covered with foil, 30 minutes (internal temperature will rise to 165°F). Remove skin before carving.