Place the rice cakes into a large bowl and cover warm water. Let the rice cakes soak for at least 10 minutes while you prep the rest of the ingredients.
Into a tall pan, like a sauté pan, add the water gochujang, gochugaru, sugar, and soy sauce. Mix well and bring it to a boil.
Once the sauce comes to a boil, drain the rice cakes and add to the sauce. Bring it back to a boil, then reduce the heat to a simmer. Let the rice cakes cook for about 5 minutes. Stir occasionally.
After 5 minutes, add the cabbage and fish cake. Let everything simmer for another 3 to 5 minutes, or until the rice cake is soft and chewy. Make sure to stir frequently to prevent the rice cakes from sticking to the bottom of the pan. Add the boiled eggs and green onions at the last minute of cooking.
Garnish the tteokbokki with sesame seeds and some sliced green onions if you wish. Enjoy while hot!
