Rinse turkey inside and out and pat dry with paper towels. Starting at the neck cavity, loosen skin over the breast by carefully slipping your hand under the skin and gently working it across the breast and down to the leg and thigh.
Using your hand, butter turkey meat under the skin, spreading butter little by little in an even layer over breast and legs. Using 4 cups stuffing, fill skin around the breast meat, distributing stuffing evenly as you go. Set turkey in pan, breast side up, on top of vegetable mixture.
Spoon about 4 cups stuffing into the large cavity through the back end of the turkey; spoon about 2 cups stuffing into the neck end. Toss remaining stuffing with 1 cup broth and spoon into a buttered 13 x 9 baking dish; cover with foil and refrigerate. Fold neck skin over stuffing and tuck it under the bird; fasten with 1 or 2 skewers. Fold wings under back of turkey so they stay in place; tie legs together with kitchen twine. Season turkey with salt and 1°2 teaspoon pepper.
Preheat oven to 350° place oven rack in lower third of oven. Combine 3 cups chicken broth and 2 cups wine in large bowl. Unfold a package of cheesecloth and fold into a rectangle 4 to 5 layers thick, large enough to cover the turkey. Submerge cheesecloth into the broth mixture and soak completely. Carefully remove cheesecloth (do not squeeze) and drape over turkey. Pour 1 cup broth mixture into pan. Roast turkey about 4 hours, basting cheesecloth every 45 minutes with broth mixture and pan juices. Carefully remove cheesecloth; roast until thigh meat registers 175° to 180° (breast meat should register 165° to 170°) on an instant-read thermometer. Turkey will be deep golden brown; juices in thickest part of thigh should run clear. Transfer turkey to a large platter, reserving pan juices; cover with foil to keep warm. Let sit at least 30 minutes before carving.
Meanwhile, bake extra stuffing in a foil-covered baking dish, about 30 minutes. Uncover and bake 20 to 30 minutes more, or until heated through and crisped on top.
To make gravy: Strain turkey drippings into a large saucepan; discard excess fat. (You should have about 4 cups pan juices). Add 1 cup broth and remaining 1°2 cup wine; bring to a boil, then reduce heat and simmer 5 minutes. Meanwhile, in a medium bowl, whisk together flour and remaining 1 cup broth until blended. Gradually whisk flour mixture into saucepan, along with remaining 1°4 teaspoon pepper. Bring back to a simmer and cook 5 more minutes, or until thickened.
To serve, cut the legs off the turkey, then the wings. On either side of the turkey, carve breast meat into slices about 1/4 inch thick. With a long spoon, remove stuffing to a serving platter. Turn the bird over and carve meat off the backside. Carve meat off the legs. Arrange dark and white meat around stuffing on the platter before serving with gravy in a boat on the side.