Chigae is a Korean Everything-in-the-Pot soup. Kimchi Chigae is, sensibly, a chigae featuring Korea's national obsession: a spicy cabbage or radish pickle called kimchi.
My introduction to chigae was in a restaurant in Seoul. Two or more people take their places around a table whose focus is a gas burner in the centre. A deep wok is placed in the middle and various ingredients added according to your preference - meat, Spam, ramen, ddok (pieces of rice 'noodle' about the size of my petite girly thumb), tofu, vegetables and of course kimchi. A lightly flavoured soup base is added, the wok covered, and the Ajuma gives fierce instructions not to touch anything. The diners entertain themselves with the usual array of side dishes until the chigae is cooked. Diners serve themselves from the wok into a bowl as they please.
Intentions tell me that the flavour of the soup comes from using older kimchi that has been pickling for too long. Tofu is a popular addition and pork is considered part of the traditional recipe. Intentions also suggests leaving the soup for a day or so* for the flavours to develop and soak into the tofu.
Like most Korean meals, chigae is made for at least two people and is expected to last a long time. It is a social and, to Western standards, intimate meal as diners serve themselves from the communal soup, share side dishes and repeatedly fill their soup bowls.
Chigae, including kimchi chigae, is easily made at home. If you have an electric frypan or electric wok you can recreate the 'middle of the table' experience of a chigae restaurant. In Australia I often buy packet soup mix for Kimchi Chigae and the kimchi itself from Asian or Korean grocers.
Warning: IANAC! My sources for this node are a not-long-enough holiday in Seoul, some Korean cookbooks and the kind proprietors of Kim's Groceries in Garema Place, Canberra.
*Leftovers? In this house?