Cut cabbage, green onion, zucchini, and mushrooms into bite-sized pieces.
Add anchovies and kelp to a pot to make a broth.
Bring the broth to a boil, then add the cabbage, green onion, mushrooms, and zucchini.
Once the vegetables are cooked, add the knife-cut noodles and boil.
Add dumplings and continue to cook until the dumplings are fully cooked through.
Season to taste and serve in a bowl.