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 simmer. Add the bean sprouts, cabbage, chicken breast, and rice noodles. Cook just until the noodles and cabbage are tender, about 5 minutes.
Before serving, stir in cilantro leaves and fish sauce. Serve with lime wedges.