Mix the turkey drippings with hot water in a saucepan over medium-low heat, stirring well to dissolve all the brown flavor bits from the drippings into the water. Whisk in the packaged brown gravy mix thoroughly, and allow the mixture to come to a simmer.
Heat the turkey fat in a skillet over medium heat, and cook the mushrooms until they release their juice, 1 to 2 minutes. Sprinkle the mushrooms with garlic powder and soy sauce, and cook, stirring occasionally, until the mushrooms have absorbed the soy sauce, 1 to 2 more minutes. Pour the mushroom mixture into the gravy, then stir well. Allow to simmer for about 10 minutes. If a thicker gravy is desired, whisk the flour into about 1/2 cup of the gravy in a small bowl, return to the saucepan, and allow to simmer for about 5 more minutes to thicken.
