Put all ingredients except miso and enoki mushrooms in a 6- to 8-qt. pot, add 4 qts. water, and bring to a boil, partly covered. Reduce heat and simmer 10 minutes, covered, to blend flavors and soften mushrooms. Put miso in a medium heatproof bowl, whisk in about 1 cup hot broth to blend, then pour into pot. Just before serving, top with enoki mushrooms.
* Find at East Asian markets or online.
Make ahead: Up to 1 day, chilled.