Brown neck and giblets: Heat the 2 tablespoons olive oil in large stockpot or Dutch oven over medium high heat. Add the turkey neck and turkey 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 1 large yellow onion quarters, 1 large carrot, 1 large celery stalk, and 3 cloves garlic. Let them brown, stirring only occasionally, to brown all sides evenly.
Deglaze: Add 1 cup dry white 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 4 cups water, 6 black peppercorns, 1 large handful fresh herbs , and 1 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.
How to make the turkey stock in the Instant Pot:
Brown neck and giblets: Heat the oil in Instant Pot on sauté mode. Add the turkey neck and turkey giblets. Allow them to cook a few minutes undisturbed to get nice and brown. Use tongs to flip and brown other side.
Brown the vegetables: Add 1 large yellow onion quarters, 1 large carrot, 1 large celery stalk, and 3 cloves garlic. Allow to brown, stirring only occasionally, to brown all sides evenly.
Deglaze: Add 1 cup dry white wine to pot and scrape bottom of pan to deglaze. Allow wine to boil and cook for a couple of minutes.
Cook stock: Add 4 cups water, 6 black peppercorns, 1 large handful fresh herbs , and 1 bay leaf to pot. 4 cups is the minimum amount of water - add more if you want more stock. Seal lid. Cook on high pressure for one hour. Quick or natural release pressure when done.
Strain and store: Strain liquid into a container. Optional: add bits of meat from the neck and minced pieces of giblets to the gravy. Refrigerate until ready to use.
To make the turkey gravy:
Make roux: In a medium or large sauce pan, 4 tablespoons unsalted butter (and/or reserved turkey drippings, if using) over medium heat. Add the same amount of flour (4 tablespoons all-purpose flour) and and whisk well to combine. Cook the roux until it is golden brown and smells wonderful.
Make gravy: Add a ladle of the 4 cups turkey stock and whisk until you have a thick paste and there are no lumps. Add another ladle and whisk again until smooth. Continue adding liquid and whisking until everything is combined and smooth.
Season to taste: Reduce heat to low and continue to cook if the gravy needs thickening. Add kosher salt and freshly ground pepper, as desired. There has been no salt added up until this point, so add a small amount, stir, taste, and repeat until it tastes right. Transfer to a gravy boat and serve hot.
Notes
Drippings are optional: You will get the most flavor if turkey drippings are used as the fat in the gravy, but butter works just as well. Just be sure that the same number of tablespoons of drippings + butter equals the number of tablespoons of flour used. My rule of thumb for gravy is 1 Tbsp fat + 1 Tbsp flour + 1 cup stock.
Giblet meat is optional: If you want gravy like grandma used to make, you can pick off the meat from the neck and chop up the giblets after making the stock and adding it to the strained stock before making the gravy. I like a smooth gravy, so I don't do this.
Water amount can vary: With most recipes, if you want to double it, you have to double all the ingredients. That is not the case with homemade stock. Simply increase the amount of water. You will not need to increase the time if using the Instant Pot, however I would increase the cooking time if using the stove or oven to extract as much flavor from the giblets as possible.
Herbs for turkey stock: The amount and type of herbs you use in your gravy can vary. You can use dried herbs, but I would use half the amount and would put them in some kind of sachet or tied cheesecloth so you can remove them later, otherwise they would be over powering. During Thanksgiving, it is common to see fresh rosemary, thyme, and sage sold together and these work perfectly.