Add oil to a large pot with cabbage and ginger and sauté for 2 minutes. Add soy sauce, 2 cups water, chicken, and stock and simmer for 5 minutes. Stir through spinach until just wilted, for about 1 minute.
Divide noodles among bowls. Ladle over soup and top with a carrot. Cut soft boiled eggs in half and place them on top to serve.