Remove the neck, giblets, and liver from the cavity of the turkey and reserve for the gravy. Rinse the turkey inside and out under cold running water.
Soak the turkey in the brine, covered and refrigerated, for at least 4 hours and up to 24 hours.
Preheat the oven to 325 degrees F.
Remove the turkey from the brine and rinse well under cold running water. Pat dry with paper towels, inside and out. Place breast side down in a large, heavy roasting pan, and rub on all sides with the butter. Season lightly inside and out with salt and pepper. Stuff the turkey with the onion, orange, celery, carrot, bay leaves, and thyme. Loosely tie the drumsticks together with kitchen string.
For the turkey broth: Heat the oil in a large heavy saucepan over medium high heat. Add the turkey neck, heart, and gizzard to the pan and saute until just beginning to brown, about 1 minute. Add the chopped vegetables and bay leaf to the pan and saute until soft, about 2 minutes. Pour the stock and 3 cups of water into the pan and bring to a boil. Lower the heat to medium-low and simmer until the stock is reduced to 4 cups, about 1 hour, adding the chopped liver to the pan during the last 15 minutes of cooking.
Strain the stock into a clean pot or large measuring cup. Pull the meat off the neck, chop the neck meat and giblets, and set aside.
Roast the turkey, uncovered, breast side down for 1 hour. Remove from the oven, turn, and baste with 1/2 cup stock. Continue roasting with the breast side up until an instant-read meat thermometer registers 165 degrees F when inserted into the largest section of thigh (avoiding the bone), about 2 3/4 to 3 hours total cooking time. Baste the turkey once every hour with 1/2 to 3/4 cup chicken or turkey stock.
Remove from the oven and place on a platter. Tent with aluminum foil and let rest for 20 minutes before carving.
For the pan gravy: Pour the reserved turkey pan juices into a glass-measuring cup and skim off the fat. Place the roasting pan on 2 stovetop burners over medium heat add the pan juice and 1 cup turkey broth and the white wine to the pan, and deglaze the pan, stirring to scrape any brown bits from the bottom of the pan. Add the remaining 3 cup of broth and bring to a simmer, then transfer to a measuring cup.
In a large heavy saucepan, melt the butter over medium high heat. Stir in the flour and cook, stirring constantly, to make a light roux. Add the hot stock, whisking constantly, then simmer until thickened, about 10 minutes. Add the reserved neck meat and giblets to the pan and adjust seasoning, to taste, with salt and black pepper. Pour into a gravy boat and serve.
To make the brining solution, dissolve the salt and sugar in 2 gallons of cold water in a non-reactive container (such as a clean bucket or large stockpot, or a clean, heavy-duty, plastic garbage bag.) Add the oranges, lemons, thyme, and rosemary.
For the brine: If you have a big turkey and need more brine than this, use 1/2 cup salt and 1/2 cup brown sugar for every gallon of water.