Pour broth and water into a large pot over medium-high heat. Add napa cabbage, carrots, snow peas, and green onions. Bring to a boil. Reduce heat to medium. Stir in fish oil and sesame oil. Simmer until vegetables are tender, at least 20 minutes.
Drop frozen wontons gently into the soup. Bring back to a boil. Reduce heat to medium; simmer until wontons are translucent, about 10 minutes. Stir in tofu, miso, salt, sriracha, and white pepper.