Remove turkey from brine. Discard brine. Pat turkey dry inside and out with paper towels. Place carrots, parsnips, celery, onion, and white turnips in bottom of a roasting pan. Place turkey, breast side up, on a rack set in a roasting pan. Fold wing tips under turkey. Let stand at room temperature for up to 2 hours.
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 into a 17-inch, 4-layer square. Immerse cheesecloth in the butter and wine; let soak.
Sprinkle 1/2 teaspoon salt and pepper inside turkey. Fill large cavity loosely with as much stuffing as it will hold comfortably; do not pack tightly. (Cook remaining stuffing in a buttered baking dish 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 the 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 the butter and wine. The skin get fragile as it browns, so baste carefully. Cook 1 more hour, basting after 30 minutes.
After the 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.
Transfer turkey to a platter, reserving pan juices. Let turkey stand 30 minutes before carving.
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