In a large saucepan, bring the vegetable broth to a boil.
Add shiitake mushrooms, bok choy, green onions, garlic, and tofu, and cook for about 10 minutes. The mixture should be at a slow simmer.
Add the udon noodles and cook according to package directions. (Mine needed to cook for about 4 minutes).
Stir in rice vinegar and sesame oil, then season with salt and pepper.
Ladle into bowls and enjoy while the soup is hot.