In a large container, add apple juice, salt, brown sugar and cinnamon sticks. Whisk until salt and sugar have dissolved.
Score the fat cap of the pork shoulder in a diamond pattern with a sharp knife. Make the slits about ¼ inch deep. Then, place the pork in the brine and ensure it's completely submerged. Refrigerate overnight or up to 24 hours.
Remove the pork from the brine, and pat it dry with paper towels. Discard the remaining brine, and season the entire pork shoulder with the BBQ rub.
Light your grill or smoker and set up for two zone cooking, establishing temperature at 225°F as read by a reliable leave-in thermometer. Add pecan and apple wood chunks to the hot coals. Then, place the pork shoulder on the grill over indirect heat. Smoke until internal temperature reaches 165°F.
Wrap the pork shoulder tightly in aluminum foil, and return to the grill over medium heat. Increase heat to 285°F and allow the pork to cook until the internal temperature reaches 205°F.
Remove the pork shoulder from the cooker, and allow it to rest for 1-2 hours before unwrapping and pulling the pork. Consider adding in additional BBQ rub while you're pulling the pork.
Add pulled pork to a bun of choice, and top with Blazin' Apple Whiskey BBQ sauce and crispy fried onions, serve hot.