Step 1: Rinse giblets thoroughly. Place giblets (excluding liver for now) and neck in a saucepan with 4 cups of broth, onion, celery, and optional herbs. Bring to a boil, then reduce heat and simmer, covered, for 1.5-2 hours, or until giblets are very tender. Add the liver for the last 15 minutes of simmering.
Step 2: Remove giblets and neck from the broth; discard onion, celery, and herbs. Strain the cooking liquid through a fine-mesh sieve into a clean bowl; set aside. Once cooled slightly, finely chop the heart, gizzard, and liver.
Step 3: In a medium saucepan, melt butter (if using) over medium heat. Whisk in the flour and cook for 1-2 minutes, stirring constantly, to create a light roux. It should smell slightly nutty. If not using butter, proceed directly to the next step with pan drippings.
Step 4: Gradually whisk in the pan drippings until smooth. Slowly add the reserved giblet broth, whisking constantly to prevent lumps. Bring the gravy to a simmer, whisking occasionally, and cook for 5-10 minutes, or until it thickens to your desired consistency.
Step 5: Stir in the finely chopped giblets. Season generously with salt and freshly ground black pepper. Taste and adjust seasoning as needed.
Step 6: Serve hot alongside your roasted poultry, mashed potatoes, or stuffing. Enjoy your rich, homemade giblet gravy!