Combine the apple cider, cranberry juice, salt, sugar, pickling spice, red pepper flakes and orange zest in a large saucepan. Bring to a simmer over medium-high heat and cook until the salt and sugar have dissolved and the spices are fragrant, 35 to 40 minutes. Stir in 8 cups ice-cold water.
Place the turkey beast skin-side down into a large bowl and pour the brine over the top. Cover and refrigerate for 3 to 4 hours (1 hour per pound).
Preheat the oven to 350 degrees F.
Remove the turkey from the brine, pat dry and place skin-side up on a roasting pan with a rack. Rub the turkey with olive oil and sprinkle with black pepper. Roast until the breast reaches an internal temperature of 160 degrees F, 1 hour 40 minutes, brushing with Cranberry Apple Glaze every 15 minutes (using about half of the glaze total).
Let the turkey rest for 10 minutes before serving with the remaining Cranberry Apple Glaze.
Cranberry Apple Glaze:
Combine the apple cider, cranberries, cranberry juice, maple syrup and apple cider vinegar in a small saucepan. Bring to a boil over medium-high heat, and then reduce to a simmer until the liquid has been reduced by 2 cups and the cranberries have burst, 18 to 20 minutes. Season with salt and pepper, and then transfer to a blender and puree until smooth. Yield: 1 1/2 cups.
Use any leftover glaze for another recipe, such as Leftover Turkey Sandwich with Spicy Cranberry Cream.