For the turkey brine: Heat the apple cider, brown sugar, salt, peppercorns, garlic, bay leaves, oranges, shallots, parsley, sage and thyme in a saucepot to dissolve the sugar and salt. Then let the mixture cool completely.
Divide the turkey pieces between two 2 1/2-gallon resealable plastic bags or containers big enough to hold them. Add equal parts of the brine to the two bags. Let rest for several hours in the fridge, preferably overnight.
Preheat the oven to 325 degrees F.
Remove the turkey from the brine and pat dry. Rub the skin with oil and sprinkle with pepper. Set the turkey on a metal rack placed over a rimmed baking sheet and cook about 15 minutes per pound, or until an instant-read thermometer inserted into the thickest part registers about 165 degrees F. The temperature will go up 5 to 10 degrees as it rests.
For the glaze: Place a small saucepot over medium-high heat. Add the apple cider, turkey stock, maple syrup, butter, peppercorns and orange rind. Bring the mixture to a light simmer and reduce by half. Baste the turkey every now and then during the last half of the cooking time.