Step 1

Brown the giblets in butter: Heat the butter in a 2-quart saucepan on medium-high heat. When hot, add the giblets to the pan. Brown them on all sides.

Step 2

Add onion, celery, carrot, garlic: Add the onion, celery and carrot and sauté until the onions turn translucent, about 3-5 minutes. Add the garlic and sauté another minute.

Step 3

Add bay leaf, thyme, water, bring to simmer: Add the bay leaf, thyme and water. Bring to a simmer. Lower the heat, partially cover so that some steam escapes, and cook on a low simmer for several hours, while the turkey (or chicken) is cooking.

Step 4

Strain the stock, mince the giblet meat: Once the bird is close to being done, strain the giblets and stock through a fine mesh sieve into a bowl. Set aside the stock. Remove the giblets from the sieve. Finely mince the giblet meat. If you want, you can pull some of the meat off of the neck and mince that as well.

Step 5

Add flour or cornstarch to roast drippings: Once the bird is done, move it to a cutting board to let it rest. Pour off the excess fat (all but a tablespoon or two) from the roasting pan. Set the roasting pan over two burners of the stovetop set over medium heat. Add the flour (or cornstarch slurry) and whisk it into the drippings. Stir in the minced giblets. Let cook for a few minutes, stirring while cooking.

Step 6

Add stock and minced giblets: Add the strained giblet stock to the pan drippings and giblets and mix well to combine. Bring to a boil and stir constantly until the gravy thickens, about 2-3 minutes. Add 1-2 teaspoons of mustard (to taste). Check for salt and add more salt to taste if needed. Serve it as-is, or purée the gravy in a blender for a smoother texture.