Soak in cold water for about 20 minutes if hardened.see note 2
Soak the rice cake slices in cold water for about 20 minutes.
(You can choose a quicker method below for making beef broth instead of step 2 and 3 if preferred.) In a large pot, bring the meat, onion, scallions and garlic to a boil in 14 cups of water. Reduce the heat to medium low, and skim off the scum. Simmer, covered, until the meat is tender enough for shredding, about an hour or longer. You can add more water if reduced too much. You'll need about about 10 cups at the end. Remove the meat and cool. Discard the vegetables. Stir in soup soy sauce, salt and pepper to taste.
Cut the cooled beef into 1 to 1.5-inch wide strips against the grain, shred, and combine well with garlic, sesame oil, and salt and pepper to taste.
To make egg garnish (jidan), separate the egg white and yolk if desired. Lightly beat the white by gently cutting it with a spoon. Stir the yolk with a spoon until smooth. Heat a lightly oiled nonstick skillet over medium low heat. Pour each egg part into a thin layer, tilting the skillet and/or spreading with a spoon. Cook each side briefly. (Do not brown the egg.) See note 2 for another egg option.
Roll each egg crepe, and slice into short thin strips. Slice the scallion diagonally into thin strips. Cut gim (seaweed sheet) into thin about 1.5-inch strips with kitchen shears, or simply crush them with hands.
Return the broth to a boil. Add the rice cake slices and boil until soft, usually about 5–8 minutes. Ladle the steaming soup into individual bowls and garnish with the shredded beef, egg, scallion and gim strips.
Quicker method for making beef broth
Instead of step 2 and 3, cut the beef into thin bite size pieces (1 to 1.5 inch). In a pot, sauté the beef with 1 tablespoon of soup soy sauce until all the pieces turn brown. Pour in 12 cups of water and bring it to a boil. Skim off the foam. Add another tablespoon of soy sauce and salt and pepper to taste. Reduce the heat to medium and continue to boil, covered, for 10 minutes, or until the meat is tender. Follow step 6 next.
If soup soy sauce, known as Joseon ganjang or guk ganjang, is not available, you can use a little bit of regular soy sauce to add color (about 1/2 tablespoon) and season with salt. Regular soy sauce is not a good substitute for Korean soups. It will make the soup too dark and a bit sweet. Fish sauce is a better substitute if available.
Although egg jidan is a classic garnish for tteokguk, a common alternative is to drizzle a lightly beaten egg over the boiling soup right before turning the heat off. Or you can omit the egg part entirely if you like.