Place carcass, wings, and bones in a small stockpot and cover with cold water. Bring to a simmer.
Place unwashed roasting pan back on a hot burner and add 2 tablespoons rendered turkey fat. Brown the garlic, onions, carrots, and celery. Add vegetables to the stockpot with the carcass with the thyme and peppercorns. Bring to a simmer and let cook for 2 to 3 hours.
Strain and remove all the bones. Save the vegetables and place back in the stockpot with the 1 quart of turkey stock. Add the leftover yams and puree with butter. Check for seasoning.
In a separate small saute pan, heat up the remaining rendered turkey fat. Saute the shiitakes and leeks together until mixture is dry and very fragrant. Chop up the shiitake-leek mixture and fold in with the sour cream, juice, and chives.
Plating: Serve in warm soup plates and place a small dollop of sour cream on top.