Soak the wood chips in water for 30 minutes, then transfer to the smoker.
Smoke the pork for 2 hours according to the manufacturer's instructions.
Combine the brown sugar, chili sauce, molasses, soy sauce, vinegar, ginger and garlic in a bowl. Season with salt and pepper and whisk until combined.
Preheat the oven to 300 degrees F (150 degrees C).
Sprinkle the pork with salt and pepper. Heat a large ovenproof skillet over medium-high heat and sear the pork on all sides. Pour half the molasses mixture over the pork. Cover and cook in the oven until the meat is so tender it falls off the bone, about 6 hours. Let rest for 30 minutes.
Remove the pork from the skillet and use a fork to pull and shred the meat (it will come off in threads). Set aside.
Skim the fat from the surface of the braising liquid. Pour the remaining molasses mixture into the skillet and cook over medium-high heat until thickened, about 5 minutes.
Pile the pork, cheese, a drizzle of the sauce, some kimchi and more cheese between the bread slices to make 4 sandwiches. Grill in a panini press.
If you don't have a smoker, you can skip that step or smoke the pork in a covered grill.
Dissolve the salt in 12 cups (3 liters) cold water. Add the cabbage and refrigerate for 4 hours.
Rinse the cabbage thoroughly under cold running water at least 3 times. Pat dry.
Bring 1 1/2 cups (375ml) water to a simmer in a skillet over medium-high heat. Add the flour and whisk for 3 minutes. Add the sugar and continue to cook, whisking, for 1 minute more.
Pulse the red pepper powder, garlic, ginger, lemongrass and onion in a food processor. Add the flour mixture and pulse to combine. Set the kimchi paste aside.
Combine the brined cabbage, chives, fish sauce, soy sauce, scallions and cucumbers in a large bowl. Stir in the kimchi paste. Refrigerate until ready to use.
You can eat it fresh, right after making it, or wait 24 hours until it has fermented.