Place the giblets and neck in a medium saucepan. Add 3 cups of the chicken or turkey broth. Bring to a boil, then reduce the heat to low. Cover and simmer for 45-60 minutes, or until the giblets are tender.

Remove the giblets and neck from the broth and set aside until cool enough to handle. Reserve the cooking broth.

Remove the meat from the neck bones and finely chop or shred it. Discard the bones.

Melt the butter or turkey drippings in a large skillet or saucepan over medium heat. Add the onion and celery and cook for 4-5 minutes, until tender.

Sprinkle the flour over the vegetables. Stir until evenly coated. Cook for about 2 minutes, stirring frequently, to remove the raw flour taste.

Gradually whisk in 3 cups of the reserved giblet broth. If you don't have a full 3 cups remaining, add enough of the reserved 1 cup of broth to make up the difference.

Add the poultry seasoning, salt, and black pepper. Bring the gravy to a gentle simmer and cook for 5-10 minutes, stirring frequently, until thickened.

Stir in the chopped giblets, neck meat, and chopped hard-boiled eggs. Simmer for another 2-3 minutes, just until everything is heated through.

Taste and adjust the salt and pepper as needed. If the gravy becomes too thick, gradually stir in additional broth until it reaches your desired consistency.