"This is a traditional dish enjoyed by many--if not all--Koreans during the New Year's and Lunar New Year holidays. Although there wasn't a lot of time for cooking or eating, I got to experience a semi-instant tteokguk for New Year's Day thanks to a good friend of mine. Garnish with green onions; add mandu (dumplings) or thin slices of beef if you like. Serve hot, as rice cakes will get soggy over time."
Heat 1 1/2 teaspoon olive oil in a nonstick skillet over medium-low heat. Beat egg yolks in a small bowl and pour into the skillet. Tilt skillet so eggs yolks spread in a thin and even sheet. Cook until set, about 1 minute per side. Transfer to a cutting board and slice into thin strips. Repeat with egg whites.
Place nori in another skillet over medium heat; toast until bright green and crispy, about 30 seconds per side. Cut into thin strips.
Rinse rice cakes in cold water; drain.
Pour beef stock into a large pot; bring to a boil. Add rice cakes and garlic. Simmer until rice cake slices are tender, about 5 minutes. Add green onions; continue cooking until rice cakes start floating to the top, 3 to 5 minutes more. Season with salt and pepper.
Ladle soup into serving bowls. Garnish with egg and nori strips.