Warm the oil in a large saucepan or stockpot over medium-high heat. Add the onion, carrots, and celery and cook until tender but not brown, about 5 minutes. Add the broth, coconut milk, ginger, chilies, garlic, and salt. Increase heat to high and bring to a boil.
Reduce heat to medium and simmer, partially covered, 15 minutes. Add the bean sprouts, cabbage, chicken, and noodles. Cook just until the noodles and cabbage are tender, about 5 minutes. Before serving, stir in cilantro leaves and Thai fish sauce. Serve with lime wedges.