Whisk the water or stock, gochujang, gochugaru, soy sauce, sugar, and garlic in a large skillet. Bring to a gentle simmer.
Taste the sauce and adjust the sweetness or heat if needed.
Simmer:
Add the rice cakes and fish cake. Simmer over medium heat for 12 to 15 minutes, stirring often, until the cakes are tender and the sauce is glossy and thick.
If the sauce thickens too quickly, add a splash of water. If it is thin, simmer uncovered for another minute or two.
Finish and serve:
Stir in half the scallions and transfer to serving bowls. Top with the remaining scallions and toasted sesame seeds.
Serve hot while the rice cakes are springy and the sauce is warm.
Notes
Soak firm rice cakes in warm water before cooking.
Adjust gochugaru to control the heat without changing the sauce texture.