In a large stock pot, combine the vegetable broth, apple juice, sea salt, rosemary, sage, thyme, and savory. Bring to a boil, stirring frequently to be sure salt is dissolved. Remove from heat, and let cool to room temperature.
Nest 1 plastic oven bag inside the other to create a double thickness Use only food grade bags such as Reynolds or the generic turkey roasting bags. Do not use plastic garbage bags, or plastic household bucketsas they are not intended for food storage and contain PCB's (PolyChlorinatedBiphenyl's ) which are not good for you to ingest. Place the double bag mouth open wide and facing up, in the roasting pan (Note: if your roasting pan will not fit in your refrigerator, use a very large bowl).
Fold back the top one-third of the double bag to make a collar (this helps keep the bags open). Place the turkey inside the double bag. Unfold the collar of the double bag and pour the brine over the bird, then the ice water water. Draw up the top of the inner bag, squeezing out as much air as possible, and secure it closed with a twist tie. Do the same with the outer bag. Turn the package so the turkey is breast side down in the roasting pan (or very large bowl) and refrigerate for at least 12 hours or up to 24 hours. Turn the turkey 3 or 4 times while it is brining.
Remove the turkey carefully draining off the excess brine and pat dry with paper towels. Discard excess brine (sanitize the sink afterwards).
Place the turkey back in the roasting pan (or on a rimmed sheet pan that is large enough to hold the turkey) and refrigerate, making sure that it touches nothing else in the fridge, uncovered, for at least 6 hours or up to overnight. This resting period allows the skin of the turkey to dry a bit so it is crisp when roasted. The turkey is now ready to be roasted.
Cook the turkey as desired reserving the drippings for gravy. Keep in mind that brined turkeys cook 20 to 30 minutes faster so watch your meat thermometer.