Boil the giblets in a small saucepan of water over medium heat until cooked, about 30 minutes. Remove the giblets, set aside, and keep the water in the saucepan.
In the same roasting pan used to cook the turkey (which should not have been cleaned!) add the reserved turkey fat. Sprinkle in the flour and whisk into the fat until it's all worked together into a paste. If the paste is too thick/clumpy, add in a little more grease. If it's too greasy, sprinkle in more flour. Whisk and cook the roux over medium-low heat until deep golden brown.
Pour in the chicken broth, whisking the whole time. Allow to cook and thicken for several minutes, whisking occasionally. If the gravy gets too thick, or if it's too salty, thin it out with a little of the giblet water. If gravy is too thin, just keep cooking it until it thickens up.
Add plenty of black pepper. Chop up the giblets and add them in. Remove as much of the neck meat as you can and add it to the gravy. Serve immediately!
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