Fill a large pot with a few quarts of water and set the neck and other giblets (not liver), the halved onion, celery, and carrot to simmering. Let it simmer several hours to make broth. I start this in the morning, before the turkey goes in the oven.

Fry up the diced onion and turkey liver in a little oil or butter. Chop it into little bits. It should be crisp. Set aside.

When you're ready to make the gravy, in a heavy pot, melt plenty of butter, and add flour a little at a time, stirring to make a medium-thick paste. Add salt and pepper. Add the giblet broth a little at a time, stirring constantly over a low heat, until it's as thin as you like it. Keep this at a very low heat until it's time to carve the turkey.

Add in the liver and onion bits, and after the turkey is removed from the pan, scrape the bottom of the pan for the wonderful savory gristle, rich little burned bits, and some of the turkey fat. Stir briskly to combine.

Add more broth if it's too thick.