Heat the oil and butter in a large saucepan over medium heat.
Add the cabbage, scallions, garlic, and ½ teaspoon salt. Cook until the cabbage is slightly softened, about 5 minutes. Remove ⅓ cup of the cabbage and set aside.
Add the broth, potatoes, and bay leaves. Simmer, covered, until the potatoes and cabbage are tender, about 15 minutes. Discard the bay leaves.
Using a blender, puree the soup until smooth. Before serving, sprinkle the soup with the reserved cabbage.