When you think about Korea's climate (it gets quite cold in the winter, in part due to its geography—70% mountainous), it makes sense that soups and stews are a huge part of the diet. Many Koreans eat a steaming bowl of soup every day, and that can be at breakfast, lunch, or dinner. Probably the most iconic is Kimchi Jjigae, a flavor-bomb combination of kimchi, pork, and tofu. If you order this at a Korean restaurant, get ready: It will likely come to the table in a hot stone bowl, still boiling, and it will continue to bubble for a couple of minutes at the table. Because this soup is so simple, the quality of the kimchi is of utmost importance. You don't want something mild and nuanced—that will create nothing but watered-down flavor in the soup. Instead, here you want to seek out the funkiest, most tangy-fermenty-stinky kimchi you can find (probably from a Korean market). And once you find that, go ahead and let it ferment some more and get even funkier. Be sure to use the cabbage itself, as well as some of the kimchi liquid; that's the good stuff.
If you want something with a little more stick-to-your-ribs heft, try a more substantial Korean stew, such as Dak Bokkeum. It's a hearty combo of chicken thighs, typical Korean flavorings (soy sauce, garlic, ginger, sesame oil, brown sugar), and gochujang, which is the real key to the flavor. There really is no sub for gochujang here; the taste is truly unique—spicy, sweet, a little fermented and earthy. You can find the Annie Chun's brand at many large supermarkets; we find it locally at Whole Foods.
And for something completely different and a little less intense, spice-wise, try Bulgogi Jungol. It's a Korean regional specialty that's basically a soup version of Korean barbecue beef (bulgogi). Beef marinates in a soy sauce mixture, then goes into a pot with glass noodles, beef stock, mushrooms, and tofu. Doesn't hurt one bit that it's rather beautiful, too.