In a large soup pot over medium heat, add the scallion whites, ginger, garlic, and sesame oil. Cook 1 minute, then add 8 cups water.
Rinse the kombu and add it to the pot with the bonito flakes. Bring to a simmer and cook 10 minutes — do not let it boil. Remove and reserve the kombu.
Add the dried shiitakes and miso and simmer gently 10 to 15 minutes, until the mushrooms are hydrated and tender.
Add the bok choy and simmer until tender, about 10 minutes. Add the tofu and cook 5 minutes more.
Ladle into bowls and garnish with the reserved scallion greens.