Rinse turkey with cool water and dry with paper towels. Let stand for 2 hours at room temperature.
Preheat oven to 450 degrees with rack in lower third. Combine melted butter and white wine in a large bowl. Fold a large piece of cheesecloth into quarters and cut into a 17-inch, four-layer square. Immerse cheesecloth in butter and wine; let soak.
Add vegetables to a large, heavy roasting pan. Place a roasting rack over vegetables. Position turkey, breast-side up, on rack. If turkey comes with a pop-up timer, remove it; an instant-read thermometer is a more accurate indication of doneness. Fold wing tips under turkey. Season cavity with salt and pepper. Fill cavities loosely with as much stuffing as they will hold comfortably; do not pack tightly. (Cook remaining stuffing in a buttered baking dish at 375 degrees.) Truss turkey with kitchen string. Fold neck flap under and secure with toothpicks. Rub turkey with softened butter and season with salt and pepper.
Lift cheesecloth out of liquid and squeeze it slightly, leaving it very damp. Spread it evenly over breast and about halfway down sides of 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 more hours, basting every 30 minutes and watching pan juices; if vegetables begin to darken, add a little chicken stock or water.
After these 2 1/2 hours of cooking, carefully remove and discard cheesecloth. Turn roasting pan so breast is facing back of 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 30 to 60 more minutes, basting after 30 minutes.
After these three hours 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 gravy. Strain pan juices into a fat separator, discarding vegetables. Let stand until fat rises to the surface, about 10 minutes, then skim it off. In a small jar, shake to combine, giblet stock and flour. Place roasting pan over medium-high heat. Add giblet stock mixture. Use a wooden spoon to scrape up browned bits from bottom of pan. Bring back to a boil, and cook until liquid has thickened slightly. Add defatted pan juices and cook over medium-high heat until thickened to desired consistency. You will have about 2 cups of gravy. Season with salt and pepper. Strain into a gravy boat. Serve with turkey.