Place frozen rice cakes in a bowl of water and soak for 10 minutes to soften.
In a bowl, combine gochujang, soy sauce, minced garlic, sugar, and gochugaru. Mix into a smooth paste.
In a pan, add water and dashi powder. Stir well and bring to a light boil.
Stir the seasoning paste into the broth and let it fully dissolve.
Add the soaked rice cakes and fish cakes (if using) to the pan. Bring to a gentle simmer and cook for 8–10 minutes, or until the sauce thickens and the rice cakes are soft and chewy.
Sprinkle mozzarella on top. Cover the pan and let the cheese melt.
Add chopped green onion and boiled egg. Serve hot and enjoy!