Put turkey giblets and neck, celery, carrot and onion in a large pot. Pour in broth, then add enough water to cover. Cover pot, bring mixture just to a boil over high heat, reduce heat to low and simmer, covered, until vegetables are tender and giblets and neck are cooked, about 45 minutes.
Remove neck and giblets from pot and, when cool enough to handle, pull meat off neck; discard bones, skin and gristle. Chop giblets. Put neck meat, giblets, vegetables and 1 cup giblet stock into blender. Puree until very smooth. (Stock and puree can be prepared ahead to this point; cover separately and refrigerate. Reheat before continuing with recipe.)
Pour juices from turkey roasting pan into a large measuring cup. Skim off fat. if there is less than 6 Tbsp. fat, add enough butter to measure to 6 Tbsp.
Place roasting pan across 2 burners. Add 1 cup of giblet stock to pan and bring to a boil. Scraping up burned bits from bottom of pan, pour into measuring cup with pan juices. Add enough giblet stock to measure a total of 6 cups liquid. (Reserve any remaining stock for another use.)
In a large saucepan, warm 6 Tbsp. turkey fat over medium heat. Whisk in flour and cook, whisking constantly until mixture turns a light caramel color, about 8 minutes. Add stock and pan juices in a thin, steady stream, whisking constantly to help prevent lumps.
Whisk in 2 Tbsp. puree mixture, bring to a boil, then reduce heat to low and cook, stirring often, until thickened, about 8 minutes. Add more puree if necessary to reach desired consistency. Season with salt and pepper. Serve with turkey.