Brown neck and giblets: Heat the oil in large stockpot or Dutch oven over medium high heat. Add the turkey neck and giblets. Allow them to cook a few minutes undisturbed to get nice and brown. Use tongs to flip and brown the other side.
Brown the vegetables: Add the onion quarters, carrot, celery, and garlic. Let them brown, stirring only occasionally, to brown all sides evenly.
Deglaze: Add wine to pot and scrape bottom of pan to deglaze. Allow wine to boil and cook for a couple of minutes.
Cook stock: Add the water, peppercorns, herbs, and bay leaf to pot. Note: 4 cups is the minimum amount of water but you can increase it. The more water you add, the longer it should cook in order to extract as much flavor as possible. Do not cover. Bring to a boil, then reduce heat to a simmer for at least one hour. The longer you cook the stock, the better it will taste. The stock can also be cooked in the oven at this point if the oven temperature can retain a very gentle simmer.
Strain and store: Strain the liquid into a container. Optional: add bits of meat from the neck and minced pieces of giblets to the gravy. Refrigerate in an airtight container until ready to use.