In a mixing bowl combine the rub ingredients. Stir until the salt and sugar have completely dissolved. Set aside.
Pour apple cider in large container or food safe bucket. Mix in half of rub ingredients and stir until sugar and salt are completely dissolved. Place pork in bucket and make sure it is almost fully immersed. Cover and refrigerate for at least 8 hours but no more then 12 hours. Cover the rest of the rub ingredients and place aside.
After the pork butt is done brining start your smoker going at 225 degrees F and preheat with the lid closed for 10-15 minutes. I used hickory chips for my smoker. When the smoked is up to temperature removed pork from the bring and set on large cookie sheet with raised edges. DO NOT DISCARD BRINE. Pat meat dry with paper towel. Rub the rest of the rub onto your pork butt, using your hands to masage the rub across every surface of the meat.
Place pork directly on your smoker grate, fat-side up, and cook for 3 hours. You will need to mop the pork with reserved brine every hour after the first hour.
Pour 4-6 cups of the remaining brine into a port and bring to a boil. This will prevent cross contamination when you mop it with this mixture. Discard the rest of the brine.
After 3 hours turn up the heat of the smoker to 250 degrees F. Transfer your roast to a large disposable aluminum foil pan and pour 2 c. of the brine liquid in the bottom of the pan. Cook an additional 6-8 hours or until an instant-red meat thermometer inserted into the thickest part of the meat registers 200 degrees. Make sure the thermometer does not touch bone.
We covered our pork after 2 hours with aluminum foil because it was browning to much.
When your pork reaches 200 degrees F, remove if from the smoker and carefully transfer it to a large cutting board. Let it rest for at least 20 minutes.
Once it rests for 20 minutes it's time to pull apart your pork. You can use you forks, Bear Paws or your hands. Discard the bone and any extra fat including the fat cap.
You can use the pork juice from the bottom of the pan to moisten the pulled pork with if you'd like.