Prepare The Pork: Preheat your oven to 325°F (165°C). Heat a large Dutch oven or oven-safe pot over medium-high heat. Season the pork shoulder with salt and pepper. Sear the pork on all sides until browned. Add the apple cider, apple cider vinegar, Chinese 5-spice powder, ginger, garlic, onion, hoisin sauce, soy sauce, honey, and sake to the pot.
Cook The Pork: Bring to a boil, then reduce heat to low, cover, and transfer to the preheated oven. Braise the pork for 3-4 hours, or until it is tender and falls apart easily. When the pork is done remove the pork from the oven and let it cool slightly. Shred the pork using two forks.
Prepare the Slaw: In a large bowl, combine the cabbage, apples, pomegranate arils, pepitas, daikon radish, and cilantro. In a separate bowl, whisk together the apple cider vinegar, pomegranate juice, lime juice, oil, and honey. Pour the dressing over the slaw and toss to coat.
Prepare The BBQ Sauce: In a saucepan, combine the ketchup, apple cider vinegar, soy sauce, brown sugar, garlic powder, onion powder, liquid smoke, dry mustard, Worcestershire sauce, pomegranate molasses, hoisin sauce, and apple cider. Bring to a boil, then reduce heat and simmer for 10-15 minutes, or until thickened.
Prepare The Aioli: In a bowl, combine the mayonnaise, Sriracha sauce, garlic, ginger, and Panda Express orange sauce. Mix well.
Assemble The Sandwiches: Toast the hamburger bun. Then put some pork on the bottom bun and top it with some BBQ sauce. Add the slaw and then top the slaw with the sriracha aioli. Serve immediately.
Enjoy your delicious pulled pork sandwiches!