In a large stockpot, combine salt, sugar, carrots, celery, onions, leeks, bay leaves, garlic, peppercorns, cumin, red-pepper flakes, cloves, and allspice. Add the water, and bring to a boil. Remove from heat. The brine needs to cool completely before the turkey is soaked in it: It can be made a day ahead or chilled over an ice bath.
Rinse turkey under cold water; pat dry. Place in stockpot, breast side down. Add brine and enough water to cover. Cover the stockpot, and refrigerate overnight. Remove turkey from brine; drain.
Preheat oven to 425 degrees. Fill cavities with stuffing, being careful not to pack too tightly. Secure skin over neck cavity with toothpicks or skewers, and tie legs together with kitchen twine. Rub turkey generously with spice butter, and place on a rack in a roasting pan.
Place in oven, and roast 30 minutes. Baste, rotate pan, and reduce oven temperature to 350 degrees. Continue basting every 30 to 45 minutes, until temperature taken in thickest part of the thigh registers 180 degrees. 31/2 to 4 hours. Once turkey is well browned, cover with foil, in sections, if necessary to prevent overbrowning. Remove foil for last 30 to 60 minutes, to crisp skin. Allow turkey to rest 30 minutes before carving. While turkey is resting, remove stuffing.
To make gravy, pour liquid from the roasting pan into a gravy skimmer; set aside. Place the roasting pan on the stove over medium-high heat; deglaze with A cup apple cider, using a wooden spoon to scrape up bits stuck to the pan. Set aside.
In a small saucepan, combine 3 tablespoons of reserved fat from pan and flour; cook 3 to 4 minutes, until browned. Add reserved apple-cider mixture, stock, and any separated juices from pan. Cook over medium heat until thickened. Serve.