Bring a pot of water to boil over medium-high heat. Add brisket and boil for 5 minutes. Skim off the scum as it boils.
After 5 minutes, remove the brisket and set aside. Clean and rinse the pot thoroughly and return to the stove.
To the clean pot, add 6 cups water, parboiled brisket, onion, Korean radish, and white part of scallions. Bring to a boil then reduce to a simmer for 20 minutes until the beef is tender. Be sure to skim away the scum floating on the top and avoid mixing the pot too frequently. This will cause the soup to turn murky.
Toss in the garlic and rice cakes. Then season the soup with fish sauce, soup soy sauce, and dashida.
Gently whisk the egg whites before slowly pouring it into the soup in a circular motion. Add the green part of scallions and season with salt and pepper to taste.
Garnishes
To prepare the egg yolks, heat a pan with 1/2 tsp of oil over medium heat. Gently whisk the egg yolks and pour it into a pan. Tilt the pan to spread the egg yolk as thinly as possible. After 1 minute, flip then cook for an additional minute. Remove and set aside to cool. Once cool, slice into thin strips.
Chili Paste (Optional)
Combine gochugaru, fish sauce and broth. Mix together until well combined.
Assemble
Garnish with thinly sliced egg yolks, seaweed strips, scallions and sesame seeds.
If you want it spicy, add a dollop of the chili paste. Serve and enjoy!