Combine the water, vegetable or bone broth, ginger, and seaweed in a pot and bring to a simmer.
Add the chopped vegetables, scallions, and daikon radish and simmer until the vegetables are soft, about 8 minutes. Remove from the heat and set aside to cool for a few minutes.
Scoop the miso into a small bowl, add a spoonful or two of broth, and mash into a paste. Add to the soup, stir, and serve.