Calvados, an apple brandy, adds a sweet finish to this gravy. The neck and giblets roasted alongside the turkey add flavor to the drippings -- discard them in step 1 for a smooth gravy, or return them to the pan at the end for a giblet gravy.
Strain drippings from roasting pan through a sieve, and press to extract liquids; reserve pan. (Shred neck meat and chop giblets if making giblet version, step 4; otherwise, discard.) Pour drippings into a glass measuring cup or a fat separator. Let stand until separated, about 10 minutes. Pour off fat.
Place pan on stove across 2 burners. Add Calvados. Bring to a simmer over medium-high heat. Cook, scraping up brown bits and stirring constantly with a wooden spoon, for 2 minutes. Add reserved drippings and 4 cups stock; bring to a simmer.
Meanwhile, whisk together remaining 1/2 cup stock and the flour until smooth. Slowly whisk stock-flour mixture into pan. Simmer until gravy is reduced by half and coats the back of a spoon, 10 to 12 minutes.
Remove from heat. Add butter, and swirl pan until butter melts. Strain gravy through a fine sieve; discard solids. Return shredded meat and chopped giblets to gravy if desired. Serve immediately or keep warm over low heat.
Gravy can be refrigerated for up to 1 week. Reheat before serving.