Make the brine: Combine 2 quarts water, the whiskey, maple syrup, salt, peppercorns, bay leaves, garlic, orange and apple peels and rosemary sprigs in a large pot. Bring to a gentle boil, stirring to dissolve the salt, then turn off the heat and cover. Allow to cool completely, then place in the fridge to chill.
Brine the turkey: Remove the turkey from its packaging and remove the bags inside that hold the neck and giblets. 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 in a large brining bag or pot. Pour in the maple-whiskey brine and refrigerate 16 to 18 hours so the brine can work its magic.
Roast the turkey: Preheat the oven to 275 degrees F. After the turkey has brined, remove it from the brining bag and rinse it thoroughly again, inside and out. Pat dry.
Truss the turkey or tuck the legs and wings, whichever you like. Place breast-side up on a rack in a large shallow roasting pan. Cover the pan with heavy-duty foil so that it's well sealed. Roast 7 to 8 minutes per pound (about 1 hour 50 minutes for a 15-pound turkey and about 2 1/2 hours for a 20-pound turkey).
Remove the turkey from the oven and increase the oven temperature to 375 degrees F. Remove the foil. (Put stuffing in the bird if you wish at this point.) Brush the butter all over the skin of the turkey, getting in the crevices. Insert a probe thermometer into the thigh, near the hip joint. Place the turkey, uncovered, back in the oven. Continue roasting, basting or brushing with the juices in the pan every 30 minutes, until the thermometer registers 165 degrees F and the juices are no longer pink. This will take about another 10 minutes per pound (about 2 1/2 hours for a 15-pound turkey and 3 to 3 1/2 hours for a 20-pound turkey). Remove the turkey from the oven and cover lightly with foil until you are ready to carve. Pour the pan drippings into a fat separator and set aside for gravy.
Place the giblets and neck in a small saucepan of water over medium heat and bring to a boil. Turn the heat to medium low and simmer 45 minutes to 1 hour, until the giblets are cooked. Remove the giblets, set aside and keep the water in the saucepan.
In the turkey roasting pan (which should not have been cleaned!), add the turkey fat. Sprinkle in the flour and whisk into the fat to form a paste. If the paste is too thick or clumpy, add a little more fat. If it's too greasy, sprinkle in more flour. Whisk and cook the roux over medium-low heat until it is deep golden brown.
Pour in the chicken broth, whiskey and maple syrup, whisking the whole time. Allow the gravy to cook and thicken for several minutes, whisking occasionally. If it gets too thick or if it's too salty, thin it with a little giblet water. If the gravy is too thin, keep cooking it until it thickens up.
Taste, then add salt and plenty of pepper. Chop the giblets and add them in, if you like. Remove as much of the neck meat as you can and add it to the gravy. Serve immediately!