Let's cook.
In a medium pot, combine the vegetable broth, chopped kimchi, gochujang, and soy sauce. Bring the mixture to a boil over medium-high heat.
Reduce the heat to medium-low and let it simmer for 5 minutes to allow the flavors to meld.
While the soup is simmering, slowly pour the beaten eggs into the simmering broth in a thin stream, stirring gently with a fork or chopsticks to create delicate egg ribbons.
Cook for 1-2 minutes until the egg is set.
Remove the pot from the heat and stir in the sesame oil.
Ladle the soup into bowls and garnish with sliced green onions before serving immediately.
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