Preparation Rinse turkey inside and out and reserve neck, giblets, and liver for another use. In a container large enough to hold turkey and 8 quarts water (we used a 5-gallon bucket lined with a large heavy-duty plastic bag) stir together water, salt, and brown sugar until solids are dissolved. Soak turkey in brine, covered and chilled, 10 hours. Remove turkey from brine and pat dry inside and out. Fold neck skin under body and fasten with a small skewer. If desired, secure wings to body with small skewers. Set an oiled metal rack in a roasting pan that will fit in covered grill. Transfer turkey to rack in pan and sprinkle with chili powder. Loosely tie drumsticks together with kitchen string. Turkey may be prepared up to this point 1 day ahead and chilled, covered. Prepare grill: Preheat gas grill. (If using a charcoal grill, open vents in lid and bottom of grill and divide 50 briquettes between 2 opposite sides of bottom, leaving middle clear. Position grill rack with wider openings over briquettes and light briquettes. They will be ready for cooking as soon as they are lightly coated with gray ash, 20 to 30 minutes.) Put turkey in roasting pan on grill and cover grill. Turn all gas settings to low. Grill-roast turkey, basting with pan juices and rotating pan 180 degrees every hour, 3 hours. (If using charcoal grill, add 10 more briquettes to each mound of coals every hour to maintain even temperature.) After 3 hours insert an instant-read thermometer in fleshy part of an inner thigh. If thermometer registers 175°F. and juices run clear when thigh is pierced, turkey is done. If turkey is not done, continue to cook (if using charcoal grill, add 10 more briquettes to each mound of coals), checking for doneness every 20 minutes. Transfer turkey to a heated platter and discard string. Loosely cover turkey with foil and let stand 20 minutes before carving. Garnish turkey with chiles, garlic, and tomatillos and serve with salsa verde.