Roasting the bones and vegetables deepens the flavor of the stock. To cool to room temperature quickly, place stock in a large stainless steel bowl set in a larger bowl of ice water; stir frequently. Store in an airtight container in the refrigerator for up to three days, or freeze for up to three months.
Preheat oven to 425°.
Cut turkey carcass into quarters. Place the turkey bones, carrot, celery, and onion on a jelly-roll pan or shallow roasting pan. Bake at 425° for 35 minutes, stirring once.
Place bones, trimmings, vegetable mixture, 4 quarts water, and remaining ingredients in a large stockpot; bring to a boil. Reduce heat, and simmer for 3 hours; skim surface occasionally, discarding solids.
Strain stock through a sieve over a large bowl; discard solids. Cool stock to room temperature. Cover and chill stock 8 hours or overnight. Skim solidified fat from surface; discard.