1. Place bonito flakes on a double layer of cheesecloth. Gather edges of cheesecloth together; tie securely. Remove and discard stems from mushrooms; thinly slice mushroom caps.
2. Combine 4 cups water and kombu in a medium saucepan; bring almost to a boil. Remove from heat; add cheesecloth bag to water. Let stand 5 minutes. Remove and discard kombu and cheesecloth bag.
3. Combine miso and 3 tablespoons soup broth in a small bowl; stir with a whisk until miso dissolves.
4. Add mushrooms and tofu to soup; cook over low heat 3 minutes or until tofu is warm. Remove from heat; stir in miso mixture and green onions. Let stand 1 minute.