Combine giblets, neck, and water in saucepan. Bring to a boil; cover, reduce heat and simmer for 1 hour or until meat is tender. Strain, reserving broth. Discard turkey neck (pull any meat remaining on the neck to include in gravy). Coarsley chop giblets; set aside. (NOTE: I PERSONALLY DON'T CARE FOR LIVER IN THIS GRAVY SO I DON'T INCLUDE IT, I DISGARD IT OR COOK IT AND GIVE MY PUPPIES A TREAT)
Skim and discard fat from reserved pan drippings of roasted turkey or hen. Add reserved broth (at least 2 1/2 cups) to pan drippings; stir until browned bits are loosened from bottom of roasting pan.
Transfer broth and dripping to a saucepan to continue cooking over a medium heat. Stir in chopped giblets; add onions, celery, salt and pepper. Bring to a boil and reduce heat. Simmer uncovered for 30 minutes.
Combine cornstarch and 1/4 cup water, stirring well; gradually stir into gravy. Bring to boil; boil for 1 minute or until thickened. Stir in boiled egg; add salt and pepper to taste. Serve hot over dressing.
NOTE: you can use flour in place of cornstarch to make a thickening base for gravy. In fact my mother always used flour, I use cornstarch. Just be sure to blend it well with small amount of water to make a paste, then add remaining water and mix well. Don't want any lumps!