Step 1:
Rinse the turkey neck and giblets. Refrigerate the liver. In a large saucepan, combine the remaining giblets, neck, and water. Add onion, carrot, parsley, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Bring to a boil. Lower the heat and simmer, covered, for 40 minutes. Add liver. Continue cooking for 20 minutes more or until tender. Strain broth, reserving 1 1/3 cups. Reserve giblets and neck, discard vegetables. When cool enough to handle, remove meat from neck; discard neck bones. Finely chop the neck meat and giblets; set aside.

Step 2:
In a Dutch oven, whisk together reserved pan drippings, milk, flour, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Cook over moderate heat until bubbly. Add the reserved broth. Cook, whisking constantly, until the mixture starts to thicken. Cook and whisk for 2 minutes more or until thickened. Stir in neck meat and giblets; heat through.

Step 3:
Roast turkey for 3 to 3 1/2 hours or until thermometer registers 180°F, basting often and covering with foil to prevent overbrowning if necessary. Bake the covered casserole of stuffing alongside turkey during the last 30 minutes of roasting, adding an additional 2 to 3 tablespoons chicken broth if stuffing is dry. Let turkey stand for 15 to 20 minutes before carving.

Step 4:
Meanwhile, cook neck and giblets for Giblet Gravy. Reserve 2 tablespoons of the pan drippings from roast turkey for Giblet Gravy. Prepare gravy. Carve turkey, discarding skin. Serve turkey and dressing with gravy.