2 tablespoons butter
1 cup diced onion
1/2 cup diced carrot
1/2 cup diced celery
1 tablespoon minced garlic
1 bay leaf
1 teaspoon dried thyme
5 cups water
Drippings from the turkey or chicken
2-3 tablespoons flour
Salt to taste
1-2 teaspoons of mustard
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.
Add the onion, celery and carrot and sauté until the onions turn translucent, about 3-5 minutes. Add the garlic and sauté another minute.
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 is cooking.
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.
Once the bird is done, move it to a cutting board to let it rest. Pour off the excess fat from the roasting pan. Set the roasting pan over two burners of the stovetop set over medium heat. Add the flour and whisk it into the drippings. Stir in the minced giblets. Let cook for a few minutes, stirring while cooking.
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 . 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.