To prepare brine:Combine apple cider, salt, peppercorns, allspice, cloves, and bay leaves in a large saucepan and bring to a boil. Cook 5 minutes until salt dissolves. Cool completely.
Remove giblets and neck from turkey, refrigerate until ready to use, and reserve for gravy. Rinse turkey with cold water and pat dry. Trim excess fat. Stuff body cavity with orange quarters. Place a turkey-sized oven bag inside a large stockpot. Place turkey inside bag. Add cold cider mixture and ice. Squeeze as much air out of bag as possible. twist top and secure with twist tie or tuck end so that it stays put. Refrigerate for 12 to 24 hours, turning occasionally.
To roast the turkey:Preheat oven or grill to 450º.
Remove turkey from bag, and discard brine, orange quarters, and bag. Rinse turkey with cold water and pat dry. Cut a small slit in the breast skin so that you can tuck wing tips under to keep in place. Tie legs together with kitchen string if the turkey didn't already come with a fastener. Place herbs in the cavity of the bird. Pour the broth in the bottom of a roasting pan that will be under the bird (this will also catch the drippings). Place roasting rack in pan if roasting in the oven or if using a rack and roasting pan on your grill. I cooked mine on the trager and put a pan on the grease tray under the rack, and the turkey directly on the rack.
Arrange turkey, breast side down, on roasting rack. Brush turkey with 1 tablespoon of the butter and sprinkle with salt and pepper. Roast at 450º for 30 minutes.
Reduce oven temperature to 350º.
Carefully turn turkey over (breast side up). Brush turkey breast with 1 tablespoon butter; sprinkle with more salt and pepper. Bake at 350º for 1 hour and 15 minutes* or until a thermometer inserted into meaty part of breast registers 150º. Remove turkey from oven, tent with foil with thermometer still inserted, and let stand until internal temperature reads 160-165º , about 20 minutes. Reserve pan drippings for gravy.