Gather all ingredients.
Combine turkey giblets, neck, and 4 cups water in a saucepan; bring to a boil. Reduce heat to low and simmer until broth is reduced to 3 cups, about 1 hour.
Strain broth and reserve 1/2 cup giblets.
Combine strained broth and turkey drippings in a saucepan over medium heat. Whisk together 1/2 cup cold water and cornstarch in a small bowl until smooth; pour into broth mixture in the saucepan and bring to a boil.
While broth is coming to a boil, finely chop giblets.
Reduce heat to low; stir giblets and hard-cooked egg into gravy.
Simmer until gravy is thickened, about 5 minutes. Season with salt and black pepper.
