Make the brine: Get out a large saucepot and add to it the apple juice, salt, and sugar. Place this over medium heat on your stove, and stir until the sugar and salt dissolve. This should take about 3 to 5 minutes. Then add this solution along with all of the other ingredients (besides the turkey) to your bucket and stir it up a little until everything is mixed well. Follow this up by adding the two turkey breasts, and make sure that they are both submerged in the brine. Finally, top this all off with The bag of ice, and put the lid on the bucket.
Let it brine: Place the bucket somewhere in your house that is relatively cool, and let it sit for 18 to 24 hours
Preheat your smoker, or grill to 275 degrees Fahrenheit, and soak your wood chips
Smoke the turkey: Take the turkey breasts out of the brine and quickly pad them dry with some paper towels. Then place both breasts on the racks of either your smoker or grill. It is at this time that you will want to add the first set of wood chips, probably just a handful. However these chips won’t last you the whole way through, so during the cooking process, you will want to periodically add more wood chips, about a handful each 30 to 45 minutes. Let the turkey breast halves cook at 275 degrees Fahrenheit for about 3 hours, however, start checking the temperature at 2 hours as some smokers/grills will cook hotter than others. You will know that both turkey breast halves have become fully cooked when their internal temperatures reach 165 degrees Fahrenheit.
Take the turkey breasts out and let them rest for 10 minutes before carving