In a pot large enough to hold the turkey, combine all of the brine ingredients and stir. Add the turkey to the pot, cover, and refrigerate for 8 to 10 hours. Remove the turkey from the pot, discard the brine, and rinse the turkey thoroughly under cold water. Pat dry.
Preheat the oven to 275 degrees.
Combine the onion, celery, apple, parsnip, quince, herbs, and spices in a bowl and toss. Spoon into the cavity of the turkey.
Truss the turkey, tying its legs together tightly with kitchen twine. Place the turkey on a roasting rack set in a large roasting pan. Cover tightly with aluminum foil, place in the oven, and roast for 2 1/2 hours.
Uncover the turkey and reserve the foil. Increase the oven temperature to 375 degrees F. Brush the turkey with half of the melted butter and cook for 30 minutes. Brush on the remaining butter and continue cooking for about 1 hour and 15 minutes longer, basting every 30 minutes, until a meat thermometer inserted in the thigh registers 150 degrees. (The internal temperature will rise 10 degrees while the turkey rests).
Transfer the turkey to a cutting board. Pour off the fat from the roasting pan. Spoon the vegetables from the cavity of the turkey into the pan; cover the turkey loosely with the reserved foil, and let rest for 30 minutes.
Meanwhile, make the gravy: Add the butter to the roasting pan with the vegetables. Place the pan over medium heat, using 2 burners if necessary. Use a wooden spoon to stir and brown the vegetables lightly, 3 to 4 minutes. Add the flour and cook for 3 more minutes, stirring occasionally. Stir in the cider, bring to a boil, and cook until reduced and thickened, 2 to 3 minutes, scraping the bottom of the pan to release the turkey drippings. Transfer the gravy to a 3-quart saucepan, add the chicken stock, and bring to a boil. Reduce the heat and simmer gently, stirring occasionally, until the gravy has thickened, about 10 minutes. Pour any juices that have accumulated around the turkey into the pan and continue cooking for 1 more minute. Season with the salt and pepper. Strain the gravy into a warm sauceboat.
Carve the turkey and serve with gravy.