Soak the rice cakes: Rinse the sliced tteok under cold water, then soak in a bowl of cool water for 10–15 minutes. This helps them cook evenly and prevents sticking.
Make the broth base: Add the beef, 9 cups of water, and the smashed garlic to a large pot.
Bring to a boil, skimming off foam for a clear broth.
Simmer gently: Lower the heat and simmer for 60–80 minutes, until the beef is tender. You should have a clean, beefy broth.
Season the broth: Remove the beef and garlic. Slice or shred the beef.
Add soy sauce, salt, and black pepper to the broth. Taste and adjust. A splash of fish sauce can add extra depth.
Prep the eggs: Beat the eggs with a pinch of salt.
You can either drizzle them in for ribbons or make a thin omelet to slice into strips (gyeran-jidan style).
Cook the tteok: Bring the broth back to a gentle boil. Drain the soaked rice cakes and add them to the pot. Cook 3–5 minutes, until they float and turn slightly translucent but still hold shape.
Add the eggs: For ribbons, slowly drizzle beaten eggs into the gently simmering soup while stirring in one direction.
For omelet strips, cook a thin egg sheet in a pan, then slice and add on top when serving.
Finish the soup: Stir in sliced scallions and sesame oil (if using). Add the shredded beef back to the pot to warm through.
Garnish and serve: Ladle into bowls. Top with crumbled roasted seaweed, extra scallions, sesame seeds, and a few grinds of black pepper.
Serve hot.