Heat the broth: Add broth to a medium pot and bring to a gentle boil over medium-high heat.
Stir in garlic, soy sauce, and fish sauce (if using).
Add rice cakes (optional): If using tteok, add them now. Simmer 4–5 minutes until they start to soften and float.
Add the mandu: Carefully slide in the frozen dumplings. Reduce to a steady simmer.
Cook 6–8 minutes, or until the dumplings float and are cooked through. Stir gently to prevent sticking.
Season the broth: Taste and adjust with a pinch of salt, more soy sauce, or a splash of water if it’s too salty. Add black pepper to taste.
Create egg ribbons: Lower the heat to just below a simmer.
With the soup swirling gently, drizzle in the beaten eggs in a thin stream while stirring slowly to create soft ribbons.
Finish with aromatics: Turn off the heat. Stir in sesame oil and most of the green onions, reserving a few for garnish.
Serve: Ladle into bowls. Top with remaining green onions, a few gim strips, and a pinch of gochugaru if you like a little heat.