Make the broth: In a medium size pot over high heat, add the anchovy stock and dried kelp and bring to a boil. Remove the kelp, lower the heat to low, and simmer for 10 minutes, uncovered.
Season the broth: Stir in gochujang, gochugaru, soy sauce and sugar – and bring back to a boil.
Cook the rice cakes: Add the tteokbokki cakes and cook for 8-10 minute, stirring frequently until they are soft.
Add the fish cakes: Add them and cook for 4 minutes, stirring frequently.
Serve. Turn off the heat and add the sesame oil and scallions. Stir and transfer to a bowl. Sprinkle sesame seeds on top and serve.
