Put the water in a large saucepan. Add 3/4 of the scallions, reserving the rest. Add the mushrooms, ginger and carrot. Bring to a boil over medium-high heat, cover, and turn the heat down to medium-low. Simmer until the vegetables are soft, about 30 minutes.
Strain the broth through a fine sieve. Remove the mushrooms from the sieve and reserve. Discard the remaining vegetables. Return the broth to the saucepan over low heat. Thinly slice the mushrooms and add them to the broth along with the remaining scallions. Stir in the miso thoroughly, never allowing the mixture to boil. Stir in the tofu. Serve warm.