In a large bowl, place pork butt. In a medium bowl, combine sugar and 1 cup salt. Rub the sugar and salt all over the meat. Cover and refrigerate 6 hours to overnight.
Preheat oven to 300 degrees F. Remove drippings from pork and place pork in large roasting pan. Roast in preheated oven until it becomes fork tender and collapses, about 6 hours. Check on the pork hourly while roasting and baste with juices from pan.
In a large bowl, whisk together scallions, ginger, oil, soy sauce, vinegar, and salt. In a medium bowl, mix together ssamjang, gochujang, vinegar, and oil.
Shuck the oysters, if using. Place each of the sauces and kimchi in serving bowls.
Preheat oven to 500 degrees In a small bowl, mix together brown sugar and tablespoon salt. Rub over the roasted pork. Cook in preheated oven until dark crust forms, 10-15 minutes.
Slice the pork and serve immediately wrapped in lettuce with rice, sauces, oysters, and kimchi.