Spread the garlic and chopped onion out over the bottom of a 5 to 6-quart slow cooker. Add the two cups of chicken broth.
In a small bowl, combine the gochujang, ginger, soy sauce, salt and pepper. Cut the pork butt into a few large pieces and rub with the gochujang mixture.
Lay the pork onto the onions and garlic in the slow cooker. Cover and cook on low for 7 to 8 hours, until the pork is tender and falling apart.
About 15 minutes before the pork is done cooking, prepare the sauce. In a small saucepan, combine the sauce ingredients and cook over medium heat until the sugar has dissolved. Set aside.
Once tender, remove the pork from the slow cooker and discard the cooking liquid. Pull the pork into shreds using two forks and toss with the Korean Sauce.
Serve the pork with thinly sliced green onion and sesame seeds on whole bib lettuce leaves. Drizzle with hoisin sauce, if desired. Serve immediately.