For the broth

1. Place a heavy-bottomed soup pot or Dutch oven over medium heat, and once hot, add the olive oil, swirling to coat the pan. Add the turkey neck and cook for 3 minutes before turning. Add the onion, carrot, and celery. Sauté for about 10 minutes, stirring frequently. Use tongs to turn the turkey neck occasionally to brown on all sides.
2. Add the turkey giblets and garlic to the pot, stir to combine, and cook for an additional 4-5 minutes, stirring as needed. Add the water, broth, vinegar, salt and pepper, and the fresh herbs (including the parsley, if using). Simmer for 45 minutes.
3. Strain the broth and discard the neck, giblets, and vegetables.

For the gravy

4. Place the same pot on the stovetop over medium heat. Add the butter (or turkey drippings), and once melted, slowly sprinkle in the flour while whisking constantly to combine with the fat. Sprinkle in the sage and continue whisking to ensure the mixture is smooth and without lumps. Cook for 3-5 minutes, until the flour is beginning to brown. Stir constantly—this is crucial to prevent the flour from burning. Slowly add the strained broth, whisking to incorporate. Once incorporated, let the gravy simmer over medium-low heat until it has thickened to desired consistency, about 10 minutes. Taste and season with salt and pepper.
5. The gravy can be stored in an airtight container in the refrigerator for up to four days. Reheat on the stovetop. Freeze for up to four months.

Note: If the gravy is prepared a day or two before cooking the turkey and you want to add turkey drippings do the following: Remove the cooked turkey from the roasting pan and transfer all liquid to a fat separator (the fat will rise to the top and the juices will settle in the bottom). Once separated, pour the juices into the gravy, whisking to combine, and reserve the fat for another use or discard.