Add the onion and kimchi and stir to combine. Add enough water to nearly cover the pork mixture (5 or 6 cups), cover, and bring to a boil. Immediately reduce the heat and simmer until the onion and kimchi are softened and the soup is quite thick, about 20 minutes.
Stir in the fish sauce (or dashida), American cheese (if using), and scallions. If it's too thick for your liking, thin the stew with water. Cover the pot and simmer for 10 minutes to combine the flavors. Serve steaming hot sprinkled with gim.
Reprinted from: The Kimchi Chronicles (c) 2011 by Marja Vongerichten. Permission granted by Rodale, Inc. Available wherever books are sold.