Special equipment: brining bag or very large pot
Remove the turkey from its packaging and remove the bags with the neck and giblets from the cavity. Rinse the neck and giblets and put them in a plastic bag in the fridge; you'll need them for the gravy. Rinse the turkey thoroughly with cold water. Place the turkey into a large brining bag or pot. Pour in My Favorite Turkey Brine and place in the fridge for 16 to 18 hours so the brine can work its magic.
Preheat the oven to 275 degrees F.
Remove the turkey from the brine and rinse thoroughly, inside and out. Soak the turkey in cold water for 15 minutes, then rinse again and pat dry.
Truss the bird or tuck the legs and wings however you like. Place the bird, breast-side up, on a rack in a large roasting pan. Cover the whole pan, tenting the bird, with heavy-duty foil so that it's well sealed. Place in the oven and roast the turkey for about 10 minutes per pound. (So, for a 20-pound turkey, about 3 1/2 hours; for a 15-pound turkey, about 2 1/2 hours.) Note: There will still be more cooking time after this, but it'll be at a different temperature.
When it's time to remove the turkey from the oven, mix together the butter, rosemary and orange zest. Remove the turkey from the oven and increase the temperature to 375 degrees F. Remove the foil and set aside. (Put stuffing in the bird if you wish at this point.) Rub the butter mixture all over the skin of the turkey, getting in the crevices. Insert an oven-safe meat thermometer into the thigh, near the hip joint. Place the turkey, uncovered, back into the oven and continue roasting, basting/brushing with the juices in the pan every 30 minutes, until the thermometer registers 165 degrees F and until the juices no longer run pink. This will take another 1 1/2 to 2 1/2 hours, depending on the size of the bird.
Remove from the oven and cover lightly with foil until you are ready to carve.
Combine the water, cider, brown sugar, salt, peppercorns, bay leaves, garlic, orange strips and rosemary in a large pot. Stir until the salt and sugar are dissolved. Bring to a boil, then cover and turn off the heat. Allow to cool completely before placing in the fridge to chill.
This is enough for a 20 pound fresh turkey. You can decrease the quantity for a smaller bird.