When oil is shimmery, add shallot, scallion whites, leek, garlic, cabbage, and potato. Add salt and pepper. Cook until onions are translucent (around 3 minutes).
Add rice cakes (either frozen or fresh) and stir until incorporated into the vegetables.
Pour in vegetable broth and bring it to a boil. Reduce heat and allow the soup to simmer until the potatoes are tender (around 12 minutes).
Add the frozen dumplings, jalapeno, and scallion greens and cook until dumplings are cooked (around 2 minutes).