In a large bucket, combine cider, 2 gallons cold water, salt and sugar, stirring well. Rinse turkey inside and out with cool water, then carefully place in bucket. Cover and refrigerate for at least 12 hours.
In a bowl, combine butter, parsley, sage, rosemary and thyme. (Can be prepared up to 2 days ahead; cover and chill. Let soften before continuing.)
Set oven rack in the lowest position; preheat to 325°F. Remove turkey from brine; pat dry with paper towels and discard brine. Place turkey breast side up on a rack in a roasting pan. Tuck wing tips under; loosely tie legs together. Sprinkle turkey all over with salt and pepper. Gently loosen breast skin with your fingers and spread 1/4 cup of butter mixture over breast meat under skin. Spread remaining herb butter over outside of turkey. Pour broth into roasting pan.
Roast turkey, basting every 30 minutes, until a meat thermometer inserted in thickest part of thigh reaches 165°F, about 3 hours. Cover breast with foil if it browns too quickly. Remove turkey from oven, transfer to a platter, cover loosely with foil and let rest for 30 minutes before carving.
Kitchen Tip: If you don't own a bucket big enough to brine your turkey, try a Reynolds™ Brining Bag.