After removing the turkey from the roasting pan, tilt the pan so the pan juices collect in one corner (don’t try to scrape the browned bits stuck to the pan; you’ll get to those later). Pour all the drippings into a large (4-cup) measuring cup and leave undisturbed until the fat rises to the top, about 5 minutes.
Pour or spoon off 1/4 cup of the risen fat, put it in a large saucepan, and set the pan aside. Spoon off and discard as much of the remaining fat as you can, carefully reserving all the pan juices underneath. Add enough giblet stock to the juices to make 3 cups; set aside.
Set the roasting pan over medium-high heat. When it’s hot, carefully pour in the Madeira, scraping up the browned bits in the pan. Keep your face away from the pan as the wine will sputter. (It’s unlikely that Madeira will ignite, but if it does, just back off and let it burn for a few seconds until the alcohol has cooked off.) Bring to a boil, simmer for 5 minutes, and then strain this liquid into the measuring cup with the giblet stock mixture; you should have about 4 cups.
Set the saucepan with the turkey fat over medium-high heat and whisk in the flour. When the flour just starts to turn blond, after about 2 min., whisk in the stock and Madeira mixture in a slow stream; continue whisking until the mixture is smooth. Simmer gently for 5 minutes and then season to taste with salt and pepper.
Reduce the heat to low and keep the gravy warm until everything else is on the table.