If the rice cakes are refrigerated or frozen, place them in warm water for 10 to 15 minutes, then drain. This softens the outside and helps the rice cakes cook evenly without splitting.

Whisk the gochujang, gochugaru, soy sauce, rice syrup, sugar, and minced garlic in a small bowl. Mixing the sauce first distributes the seasonings evenly through the broth.

Pour the broth into a wide skillet or shallow pot and bring it to a gentle boil. Stir in the prepared sauce and cook for 2 minutes so the garlic and pepper flavors begin to bloom.

Add the rice cakes and cabbage to the seasoned broth, stirring carefully to coat them. Simmer uncovered for 8 to 10 minutes, stirring every few minutes so the sauce does not settle on the bottom.

Add the sliced fish cakes and continue simmering for another 8 to 12 minutes. The rice cakes are ready when they are soft and chewy in the center and the sauce has thickened enough to cling to a spoon.

Taste the sauce and adjust it with a little more sugar for sweetness, gochujang for heat, or broth if it has become too thick. Keep the pan at a gentle simmer because vigorous boiling can make the rice cakes overly soft.

Turn off the heat and stir in most of the green onions. Let the tteokbokki stand for 2 minutes so the sauce thickens slightly while the fresh onion flavor remains bright.

Spoon the Korean rice cakes into serving bowls and finish with the remaining green onions and toasted sesame seeds. Serve immediately while the sauce is glossy and the rice cakes are warm and springy.