Add water, dried anchovies and kelp to a shallow pan. Bring to a boil and simmer for 15 minutes. Discard kelp and anchovies.
Add sauce mixture to the pan and stir thoroughly.
Add rice cakes, fish cakes, carrots, and green onion. Stir gently and cook until rice cakes soften and sauce thickens.
Stir in dumplings (be careful not to break) and eggs. Remove from heat. Garnish with fresh green onion. Eat immediately.