If your rice cakes are frozen or firm, soak them in warm water for 10 to 15 minutes. Drain and set aside.
In a small bowl, whisk together the gochujang, gochugaru, low-sodium soy sauce, granulated sugar, and minced garlic until smooth.
In a medium saucepan over medium heat, combine the water or vegetable broth and the chopped white parts of the scallions. Bring to a gentle simmer.
Stir the sauce mixture into the simmering liquid until fully dissolved.
Add the drained rice cakes and fish cakes (if using), stirring to coat them evenly in the sauce.
Simmer for 10 to 15 minutes, stirring occasionally, until the sauce thickens and the rice cakes are soft and chewy.
Remove from heat and divide into bowls. Sprinkle the sliced green parts of the scallions on top before serving.