Preheat oven to 325°. In a 1- to 2-quart pan over medium heat, melt butter. Stir in half the oregano and thyme and the minced garlic. Remove from heat.
Remove and discard leg truss from turkey. Pull off and discard any lumps of fat. Remove giblets and neck (they're often packed in neck or body cavity) and save for gravy or discard. Rinse turkey inside and out; pat dry. Lightly sprinkle turkey cavities with salt and pepper and remaining oregano and thyme.
Rinse chiles and pat dry. Cut off stems and shake out seeds (cut chiles, if necessary, to remove seeds easily). Peel onion and cut into 1-inch wedges. Rinse garlic head and cut in half crosswise. Place half the chiles, onion, and garlic in turkey body cavity. Set a V-shaped rack in a 12- by 17-inch roasting pan. Place remaining chiles under center of rack. Set turkey, breast up, on rack. If desired, tuck wing tips under body and loosely tie ends of drumsticks together with cotton string. If turkey overlaps pan rim, tuck a strip of heavy-duty foil along pan sides to keep fat from dripping over. Brush turkey all over with butter mixture. Sprinkle lightly with salt and pepper. Lay remaining onion and garlic, cut side down, in pan. Pour 2 cups broth into pan.
Roast turkey until a meat thermometer inserted straight down through thickest part of breast to the bone registers 160°, 2 to 3 hours. Check pan occasionally; if most of the broth has evaporated, add 1 to 2 cups more broth so pan drippings don't burn. Tip turkey slightly to drain juices from body cavity into pan. Transfer to a platter. Let stand in a warm place, uncovered, for 15 to 30 minutes.
Meanwhile, pour pan juices into a 2- to 4-cup glass measure. Skim off and discard fat. Pour 2 cups of the pan juices (if you don't have enough, add more broth to make 2 cups) into a blender. Add onion and chiles from turkey cavity and pan. If desired, squeeze garlic from skins into blender, or discard garlic head. Holding blender lid down with a towel, whirl until mixture is coarsely puréed. Return sauce to roasting pan and stir over medium heat until hot. Add salt to taste and pour into a bowl.
Carve turkey and serve with chile sauce. If thigh joints are still pink (common in an oven-roasted bird), cut drumsticks from thighs, place thighs in a baking pan, and bake in a 350° to 450° oven until no longer pink, 10 to 15 minutes, or put on a microwave-safe plate and cook in a microwave oven at full power (100%) for 1 to 3 minutes.