Cut a potato into a 1/4" (6 mm) thick bite size pieces. Peel and cut carrot vertically in half, then slice thinly. Cut Nappa cabbage into 1" (2.4 mm) wide strips. Slice green onions thinly.
Boil Dashi at medium heat, add vegetables except green onions, and cook until tender.
Turn down the heat to low, then add Miso paste, and let it dissolve in the soup. Just before serving, add green onions.