In a large pot saute the mushrooms, onion, garlic and ginger in sesame oil for about 10 minutes.
Add the broth, sweet potato, and carrot. Bring to a boil. Reduce heat. Cook for about 10 minutes, uncovered.
Add the noodles, cook until soft (2-5 minutes). Don't overcook noodles.
In a seperate bowl, combine the milk and miso. Whisk. Stir into soup.
Add tofu, peas, and vinegar.
Serve garnished with scallions and nori.