In a large pot, combine apple cider, water, orange juice, kosher salt, pepper, bay leaves, rosemary, thyme, garlic and onion. Bring to a simmer over high heat. You do not need to rapidly boil the liquid; just whisk to make sure that the salt is dissolved. Remove from heat and allow the brine to cool completely (this can take quite a few hours).
Add turkey to cool brine, cover and refrigerate for 12-14 hours (or up to 24 hours).
Before removing turkey from brine, adjust oven rack to lowest position. Heat oven to 350 degrees F.
Place a rack in a large roasting pan. You can line the roasting pan with foil first, for easy cleanup. Place 1 cup of water in the bottom of the pan. Set aside.
Remove turkey from brine and rinse under cool water. Pat inside and outside of the turkey dry with paper towels. Tie legs with kitchen twine, and tuck wing tips behind back. Brush outside of the turkey with melted butter. Set turkey breast-side up on the rack in the roasting pan.
Roast turkey, uncovered, until thickest part of the breast registers 165 degrees and thickest part of thigh registers 170 to 175 degrees on instant-read thermometer. Keep a close eye on the turkey after the first 30-60 minutes of roasting – the skin will get dark quickly. Once the skin is nicely browned to your liking, tent the turkey with foil (shiny side up) to prevent burning while it finishes cooking.
The total cooking time will vary depending on the size of your turkey, on how cold your turkey is when it goes in the oven, and on your individual oven. The following cooking times are only estimates. If your turkey is not close to room temperature when it goes in the oven, it will take longer to cook. If it is at room temp, it may take less time to cook. So check the temperature early. A brined 12 -14 lb. turkey needs about 2 ½ - 3 hours in a 350 degree F oven, while a 15-16 lb. turkey will likely require closer to 3 - 3 ½ hours. Again, I've had a brined 15-lb. turkey cook in as little as about 2 ½ hours, so it's always best to check the temperature of the meat early.
Transfer turkey to a cutting board and allow to rest for 30-40 minutes. Carve and serve.