In large pot, bring at least 3 qts water to a boil. Slowly add soba. When water returns to a boil, add 1/2 c cold water. Repeat steps of returning water to a boil and adding cold water 2 or 3 times, until the noodles are just tender (it will take 5 to 7 minutes total.) Drain and rinse well, working your fingers through the strands to separate them. Set aside.
Combine chicken broth and ginger in the large pot and bring to a boil. Reduce the heat to medium-low, add mushrooms and simmer for 8 minutes. Add sake or mirin, tamari or soy sauce and rice-wine vinegar. In a small bowl, whisk a ladleful of the broth with miso to dissolve it; return the mixture to the pot, along with spinach. Simmer for 2 minutes more and remove from the heat. Divide the noodles among soup bowls and ladle the soup over the top. Garnish with scallions and daikon.