Korean Egg Toast (Gaeran Tost-u)

My lunch today was Korean egg toast.

This Korean breakfast sandwich, sold by street vendors in cities, is commonly called tost-u (toast) or gaeran tost-u (egg toast). It's not that different from an American egg sandwich, but the addition of cabbage and a sweet dusting of brown sugar are tasty Korean additions. It is Korean fusion cooking at the street level. Here is my process for making it.