The secret to rich stock is roasting the bones and vegetables. To encourage caramelization, cut the carcass into pieces that lie as flat as possible in the pan. If your turkey was larger than 12 pounds, you may have to cut it into smaller pieces than the recipe instructs.
Preheat oven to 425°.
Cut the turkey carcass into quarters. Place the carcass, skin, carrots, celery, onion, and garlic on a jelly roll pan or shallow roasting pan. Bake at 425° for 45 minutes, stirring once.
Place turkey and vegetable mixture, water, broth, and peppercorns in a large stockpot. Bring to a boil; cover, reduce heat, and simmer 2 hours. Strain mixture through a sieve into a bowl, reserving stock. Discard solids. Cover and chill stock 8 hours or overnight. Skim solidified fat from surface; discard fat.
Note: Store the turkey stock in an airtight container in the refrigerator for up to a week, or freeze for up to 3 months.