Reserve the turkey's giblets and neck, if desired, for making Turkey Stock.
Preheat oven to 425 degrees, with only one rack in the lowest position. Stir together melted butter and wine in a bowl. Fold a very large piece of cheesecloth into quarters so that it is large enough to cover breast and halfway down sides of turkey. Immerse cloth in butter mixture.
Place turkey, breast side up, on a rack in a roasting pan. Fold wing tips under. Season inside turkey with salt and pepper. Loosely fill body and neck cavities with stuffing. Tie legs together with kitchen twine. Fold neck flap under; secure with toothpicks. Rub turkey all over with the 4 tablespoons softened butter; season with salt and pepper.
Remove cheesecloth from butter mixture, squeezing gently into bowl; reserve butter mixture for brushing. Lay cheesecloth over turkey. Place turkey, legs first, into oven. Roast 30 minutes. Brush cheesecloth and exposed turkey with butter mixture. Reduce temperature to 350 degrees. Roast, brushing with butter mixture every 30 minutes and rotating once, 2 1/2 hours; tent with foil if browning too quickly. Pour 1/2 cup water into pan if juices are very dark brown.
Discard cheesecloth; rotate pan. Baste turkey with pan juices. Roast, rotating pan halfway through, until skin is golden brown and an instant-read thermometer inserted into thickest part of thigh (and the stuffing) registers 165 degrees, 1 1/2 to 2 hours more, basting turkey every 30 minutes. Transfer to a platter. Let turkey stand at room temperature 30 minutes, tented with foil, before carving. Garnish with herbs if desired.