Prep the Rice Cakes
If using refrigerated or frozen rice cakes, soak them in warm water for 10–15 minutes to soften. Drain before using.
In a small bowl, combine the gochujang, gochugaru, soy sauce, sugar (or syrup), and minced garlic until smooth.
Pour 2 cups of broth into a shallow pan or pot over medium-high heat. Stir in the sauce mixture until fully dissolved and bring to a boil.
Add the drained rice cakes, fish cake pieces, and hard-boiled eggs. Reduce heat to medium and simmer for 8–10 minutes, stirring frequently so the rice cakes don’t stick to the bottom.
Once the sauce thickens to a glossy consistency and the rice cakes are soft and chewy, fold in the green onions. Cook for another 1 minute. Garnish with toasted sesame seeds and serve hot.