Soak the sliced rice cake in cold water for 20 to 30 minutes if it's been refrigerated or frozen, until the pieces separate easily and feel pliable rather than stiff.
Marinate the beef 10 minutes in 1 tbsp of the soy sauce, half the garlic, and the sesame oil.
Brown the beef in a dry pot over medium heat for 2 to 3 minutes, then add the water and bring to a boil.
Skim the foam that rises in the first few minutes, then lower the heat and simmer 15 minutes so the broth takes on the meat's flavor.
Meanwhile, make the jidan: fry the egg whites and yolks separately in a barely-oiled pan, as thin as you can manage, then stack and slice into fine strips.
Add the remaining garlic and the drained rice cake to the simmering broth and cook 4 to 5 minutes, until the pieces float and turn tender but still chewy at the center.
Season with the remaining soy sauce, salt and pepper to taste.
Ladle into bowls, top with the egg strips, seaweed and scallions, and serve right away, while the rice cake is still soft.
