1. Make the brine: Put ingredients into a large, wide stockpot. Add 4 quarts plus 2 cups cold water. Bring to a boil, stirring until sugar and salt have dissolved. Remove from heat; let cool completely.

2. Submerge turkey, breast side down, in brine. Cover; refrigerate 24 hours, turning turkey once. Remove turkey, and pat dry with paper towels. Let stand at room temperature 2 hours. Discard brine.

3. Preheat oven to 425 degrees, with rack in lowest position. Stir 12 tablespoons melted butter and the wine in a medium 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.

4. 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 (about 5 cups in the body and about 1 cup in the neck). Tie legs together with kitchen twine. Fold neck flap under; secure with toothpicks. Rub turkey all over with 1/4 cup softened butter; season with salt and pepper.

5. 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.

6. 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 the thickest part of the thigh registers 165 degrees (stuffing should also register 165 degrees), 1 1/2 to 2 hours more. Stir remaining 2 tablespoons melted butter and the quince syrup in a bowl; brush over turkey during last 10 minutes in oven. Transfer to a platter. Set pan drippings aside for gravy. Let turkey stand at room temperature 30 minutes, tented with foil, before carving. Garnish with quinces and thyme.