"It's been a long time since we've eaten tteokguk (rice cake soup) so it was a pleasant surprise when the wife took over the reins in the kitchen and surprised me and the kids with this delicious Korean soup. Tteokguk is a traditional dish enjoyed by many (if not all Koreans) during the Lunar New Year holiday. The rice cake used to make tteokguk is first made into a long, white cylinder shape called garae tteok. Its shape and length is symbolic, wishing for longevity in life."
Combine water and beef strips in a stockpot; bring to a boil. Reduce to medium-high heat and simmer, skimming off any foam from the top. Add onion and garlic; simmer stock until flavors combine, 15 to 20 minutes.
Rinse rice cake slices in cold water and drain well. Stir rice cakes and soy sauce into the stock; bring to a gentle boil until rice cake slices start to float, 8 to 10 minutes. Season with salt and pepper. Stir eggs and green onions into the stock. Ladle into bowls.
Optional (but recommended) garnishes for the soup: 1 teaspoon sesame oil, 2 eggs (fry yolks and whites separately into thin sheets and slice into strips), and seaweed strips (toast seaweed sheets in a skillet over medium heat until crispy; cut into thin strips).
Most Koreans include mandu (dumplings) with tteokguk to make it heartier. If doing so, simply add them in the broth a few minutes before the rice cakes. They are available at Korean grocers and supermarkets with well-stocked Asian food sections.