Rinse giblets and neck. Wrap liver airtight and chill to add later, or save for other uses. Chop giblets and cut neck into 3 or 4 pieces.
In a 5- to 6-quart pan over high heat, combine chopped giblets, neck, onions, carrots, celery, and 1/2 cup broth. Boil and stir often until meat and vegetables are very well browned, 15 to 20 minutes. Add another 1/2 cup broth, scrape drippings free, and repeat step.
Add 9 cups broth, bay leaf, port, and pepper, stirring to scrape browned bits free. Cover and simmer until giblets are very tender when pierced, about 1 1/2 hours. If desired, add the liver and simmer 10 more minutes.
Pour broth through a fine strainer into a bowl. Discard vegetables. Measure broth. If you have more than 8 cups, boil to reduce; if you have less, add more chicken broth.
Pull meat off neck; discard bones. Finely chop meat and giblets (optional).
Smoothly blend cornstarch with 2/3 cup water. Add to broth in pan and stir over high heat until gravy is boiling, about 5 minutes. If desired, scrape turkey drippings into gravy and stir until boiling. Add giblets, if desired, and stir 1 to 2 minutes more. Pour into a bowl. Add salt to taste.