Pour apple cider and ½ cup barbecue sauce into a 5- or 6-quart slow cooker and stir until combined. Add garlic, onion, and pork. Cook on low until meat is very tender and shreds easily with a fork, about 7-8 hours.
While the meat is cooking, combine all slaw ingredients in a large bowl and mix. Refrigerate at least 30 minutes, but preferably 3-4 hours.
Once the meat is done, shred with two forks and add remaining ½ cup barbecue sauce. Toast bread slices. Place meat on top of one slice of bread, add slaw, top with remaining bread slice, and serve.
Reserve at least 1 cup of pulled pork for meal 2. The slaw is also still good the following day.