In a medium pot, combine 3 cups of dashi, 2 tablespoons of sake, 1 tablespoon of soy sauce, and ¼ teaspoon of salt. Heat over medium-high until the mixture comes to a boil, which should take about 5 minutes.

Once the broth is boiling, stir in 150 grams of sliced napa cabbage, the white parts of 30 grams of scallions, and 50 grams of sliced shiitake mushrooms. Reduce the heat to medium and let the vegetables simmer until they are tender, around 10-12 minutes.

While the vegetables are cooking, fill another pot with water and bring it to a rolling boil over high heat. Gently add 12 gyoza dumplings, cooking until they float to the surface, approximately 1 minute.

Using a slotted spoon, transfer the boiled gyoza into the pot with the simmering broth and vegetables. Allow the soup to cook for an additional 2-3 minutes.

Stir in the green parts of the scallions and 1 teaspoon of toasted sesame oil to add a rich aroma. Ladle the soup into bowls and serve.