Make the spice rub:
In a small bowl, stir together brown sugar, ground ginger, salt, garlic salt, black pepper and red pepper.
Make the pulled pork:
Rub pork with the spice rub. Wrap in plastic wrap and refrigerate overnight. Let the pork stand at room temperature for at least 1 hour before preparing.
Make the slaw:
In a large bowl, toss together cabbages, bell pepper, vinegar, onion, sugar, oil, mayonnaise, celery seed, salt and mustard. Serve pork on buns topped with slaw.
Set the Multi-Function Cooker to Sear/Sauté Mode, HIGH. Press Start. Add oil to the Multi-Function Cooker. Place pork in the Multi-Function Cooker when oil is shimmering. Cook for 3 to 4 minutes per side.
Set the Multi-Function Cooker to Program 2 Mode. Add ginger beer, vinegar and garlic. Cover and set the Multi-Function Cooker to Program 1 on HIGH for 1 hour. Set Program 2 on MEDIUM for 5 hours. Press Start. Cook for 6 hours. Shred pork, and discard fat and bones. Toss pork in the drippings for additional flavor.