Cut the fish cake, onion, green onion, spicy chili pepper, and carrot into bite-sized pieces.
Add cooking oil to a pot, then stir-fry minced garlic and chili oil.
Add the onion, carrot, green onion, and spicy chili pepper, and stir-fry together.
Add red pepper powder and stir-fry gently over low heat.
Add water, kelp, and anchovies, bring to a boil, then remove the solids to make the broth.
Add fish cake to the broth and let it simmer once.
Season with soy sauce, salt, and black pepper.
Garnish with green onion and boil one more time before serving.