This is my version of the giblet gravy my grandaddy would make every year for Christmas. Feel free to modify; this is just a starting point, and everyone's tastes differ. (For example, while you can puree giblet gravy for a smoother texture, I like my chunks large enough to be fun, tasty, and identifiable.) Leave a comment and let me know how it goes!
Step 1: Saute giblets
The main body cavity usually houses the neck and tail; a bag of smaller parts may be in the chest cavity or tucked under the skin at the neck. This smaller bag should contain a liver (the big purple blob), the heart, and the gizzard.
Dump the lot into a hot, oiled pan with some pepper and a bay leaf. When you've browned the bits on all sides add a coarsely-chopped onion or two and stir.
Step 2: Deglaze and boil
Simmer and stir to remove any crispy bits from the bottom, then add 2 eggs, vegetables, and water to cover. Simmer for a while, replenishing the liquid as necessary. The eggs will thoroughly hardboil during the process.
2-3 carrots, coarsely chopped
2-3 ribs celery, coarsely chopped
*Sherry is a sweet fortified wine; any similar beverage will do. The alcohol cooks off entirely, so it's the sugars and taste complexity you're after.
Step 3: Chop giblets
Chop the liver, heart, gizzard, veggies, and eggs (after peeling). Pull meat from the neck and tail, and chop it into bits as well. Set aside. You'll probably want smaller chunks than I've used below; I was just a bit lazy.