Soak the rice cakes. If your tteok is firm or refrigerated, soak in warm water for 10–15 minutes to soften. Drain before using.
Fresh tteok usually doesn’t need soaking.
Make the sauce base. In a small bowl, mix gochujang, gochugaru, soy sauce, sugar, garlic, and sesame oil until smooth. Adjust the gochugaru based on your spice preference.
Start the broth. In a wide pan or shallow pot, bring water or stock to a gentle boil over medium heat. Add the onion and the white parts of the green onions.
Let it simmer for 2–3 minutes to soften.
Add the sauce. Stir the sauce mixture into the simmering liquid until fully dissolved. Taste and adjust sweetness or saltiness as needed.
Cook the rice cakes. Add the drained rice cakes. Keep the heat at a steady simmer and stir often to prevent sticking.
Cook for 7–10 minutes, until the tteok is soft and chewy.
Add mix-ins. Stir in fish cake, cabbage, and boiled eggs if using. Simmer 2–3 more minutes so the flavors meld. If the sauce gets too thick, add a splash of water or stock.
Finish and thicken. When the sauce looks glossy and coats the rice cakes, turn off the heat.
Stir in a teaspoon of neutral oil if you want extra shine and a silky finish.
Garnish and serve. Top with sesame seeds and the green parts of the green onions. Serve hot, straight from the pan.