How to Make It
In a very large stockpot, combine the water with 1/4 cup of kosher salt and stir until the salt dissolves. Add the turkey, breast down; refrigerate for 2 days. Remove the turkey from the brine and dry it inside and out with paper towels. Bring the bird to room temperature and season with salt and pepper.
Preheat the oven to 425°. Loosely fill the main and neck cavities of the turkey with about 10 cups of the Apple-Chestnut Stuffing. Spread the remaining stuffing in a buttered large, shallow glass or porcelain baking dish; cover with plastic wrap and refrigerate.
Pour 1 cup of the stock into a large roasting pan and set the turkey in the pan. Add the butter to the pan and roast the turkey for 30 minutes. Baste with the pan juices. Reduce the oven temperature to 350° and roast for 45 minutes. Add the apple cider to the pan, baste the turkey and roast for about 1 hour and 15 minutes, or until the skin is richly browned; if the skin on the legs browns too quickly, cover them with foil. Baste again and cover the whole bird with foil. Roast the turkey for about 1 hour and 20 minutes longer, or until an instant-read thermometer inserted in an inner thigh registers 170° and the stuffing registers 165°. Transfer the turkey to a carving board and cover the bird loosely with foil.
Increase the oven temperature to 400°. Bake the stuffing in the baking dish for 20 minutes, or until cooked through and crisp on top.
Meanwhile, pour the juices from the roasting pan into a 1-quart glass measuring cup; skim off the fat and reserve. Set the roasting pan over 2 burners on moderately high heat. Add the remaining 2 cups of stock to the pan and bring to a simmer, scraping up the browned bits from the sides and bottom with a wooden spoon. Reduce the heat to moderate and cook for 4 minutes. Add the stock in the roasting pan to the juices in the measuring cup.
Strain the pan juices into a medium saucepan. Spoon 1/4 cup of the reserved turkey fat into a small bowl and whisk in the flour. Whisk 1 cup of the pan juices into the flour mixture until smooth. Whisk the mixture into the pan juices in the saucepan and bring to a boil over moderately high heat, whisking often. Add the Calvados and simmer, whisking occasionally, until no floury taste remains, about 5 minutes. Season the gravy with salt and pepper and transfer to a warmed gravy boat. Carve the turkey and serve with the stuffing and gravy.