Heat the oil in a large heavy saucepan over medium high heat. Add the turkey neck, heart, and gizzard to the pan and saute until just beginning to brown, about 1 minute. Add the chopped vegetables and bay leaf to the pan and saute until soft, about 2 minutes. Pour the stock and 3 cups of water into the pan and bring to a boil. Lower the heat to medium-low and simmer until the stock is reduced to 4 cups, about 1 hour, adding the chopped liver to the pan during the last 15 minutes of cooking.
Strain the stock into a clean pot or large measuring cup. Pull the meat off the neck, chop the neck meat and giblets, and set aside.
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