In a pot, combine the kombu and water to cover and bring to a boil. Remove the kelp and discard. Add the bonito flakes, stir well, and remove from the heat. Let the flakes settle to the bottom of the pot. Strain the stock through a fine sieve, discarding the bonito flakes. Return the stock to the pot and add the mushrooms.
Cook over moderate heat for about 3 minutes, or until the mushrooms have softened. In a small bowl, stir together a ladle of stock with the miso and stir the mixture into soup. Divide the soup among 4 bowls and sprinkle with the reserved enoki and the scallions.