While the turkey rests, make the gravy: Use a fine-mesh strainer to strain the turkey pan drippings into a medium bowl, leaving behind any browned bits, or "fond," stuck to the pan. Press down on the solids to get as much liquid as possible into the bowl; discard the solids. Pour the liquid into a measuring cup or a fat separator and allow the fat to rise to the top. Meanwhile, place the roasting pan across two burners over medium-low heat. When the pan is sizzling, add the wine and stir, scraping up all the fond in the pan. Turn off the heat and pour the wine mixture through a fine-mesh strainer set over a bowl.
Ladle or spoon off the fat from the pan drippings and discard; set aside the jus. In a saucepan over low heat, melt the butter. Then sprinkle in the flour and whisk until the flour is completely incorporated and light golden brown, 1–2 minutes. Slowly add the wine mixture, whisking constantly. When it has fully absorbed into the roux, slowly add the reserved jus. Small additions of liquid and continuous whisking are the keys to smooth gravy.
Finish the gravy by adding turkey or chicken stock a ½ cup at a time and whisking; taste and adjust the seasoning with salt and pepper as you go. (You’ll need a total of 2½–3 cups of liquid to make the gravy.) When the gravy is thick yet pourable and perfectly seasoned to taste, transfer it to a bowl or gravy boat and serve immediately.