Rinse turkey with cool water, and dry with paper towels. Let stand for 2 hours at room temperature.
Place rack on lowest level in oven. Heat oven to 450 degrees. Combine melted butter and white wine in a bowl. Fold a large piece of cheesecloth into quarters and cut it into a 17-inch, 4-layer square. Immerse cheesecloth in the butter and wine; let soak.
Place turkey, breast side up, on a roasting rack in a heavy metal roasting pan. If the turkey comes with a pop-up timer, remove it; an instant-read thermometer is a much more accurate indication of doneness. Fold wing tips under turkey. Sprinkle 1/2 teaspoon each salt and pepper inside turkey. Fill large cavity and neck cavity loosely with as much stuffing as they hold comfortably; do not pack tightly. (Cook remaining stuffing in a buttered baking dish for 45 minutes at 375 degrees.) Tie legs together loosely with kitchen string (a bow will be easy to untie later). Fold neck flap under, and secure with toothpicks. Rub turkey with the softened butter, and sprinkle with remaining 1 1/2 teaspoons salt and pepper.
Lift cheesecloth out of liquid, and squeeze it slightly, leaving it very damp. Spread it evenly over the breast and about halfway down the sides of the turkey; it can cover some of the leg area. Place turkey, legs first, in oven. Cook for 30 minutes. Using a pastry brush, baste cheesecloth and exposed parts of turkey with butter and wine. Reduce oven temperature to 350 degrees and continue to cook for 2 1/2 more hours, basting every 30 minutes and watching pan juices; if the pan gets too full, spoon out juices, reserving them for gravy.
After this third hour of cooking, carefully remove and discard cheesecloth. Turn roasting pan so that the breast is facing the back of the oven. Baste turkey with pan juices. If there are not enough juices, continue to use butter and wine. The skin gets fragile as it browns, so baste carefully. Cook 1 more hour, basting after 30 minutes.
After this fourth hour of cooking, insert an instant-read thermometer into the thickest part of the thigh. Do not poke into a bone. The temperature should reach 180 degrees (stuffing should be between 140 degrees and 160 degrees) and the turkey should be golden brown. The breast does not need to be checked for temperature. If legs are not yet fully cooked, baste turkey, return to oven, and cook another 20 to 30 minutes.
When fully cooked, transfer turkey to a serving platter, and let rest for about 30 minutes. Meanwhile, make the gravy. Pour all the pan juices into a glass measuring cup. Let stand until grease rises to the surface, about 10 minutes, then skim it off. Meanwhile, place roasting pan over medium-high heat. Add 1 cup dry red or white wine, or water, to the pan. Using a wooden spoon, scrape the pan until liquid boils and all the crisp bits are unstuck from pan. Add giblet stock to pan. Stir well, and bring back to a boil. Cook until liquid has reduced by half, about 10 minutes. Add the defatted pan juices, and cook over medium-high heat 10 minutes more. You will have about 2 1/2 cups of gravy. Season to taste, strain into a warm gravy boat, and serve with turkey.