Boil the taro, carrots, and mushrooms (if you decide to use them) in the dashi stock for roughly 10 minutes, until soft enough to be pierced with a toothpick.
Take a few tablespoons of the hot stock out of the pot and combine with the miso in a small bowl. When thoroughly blended, incorporate back into the soup.
Meanwhile toast the mochi until they begin to swell. Then add them to the soup, swirl around until warmed, and turn off the heat.
To serve, pour the soup into four deep bowls, making sure there are two mochi in the middle of each bowl. At the last moment, add any greens, and top with a sliver or two of yuzu peel and a sprinkling of bonito flakes. Serve immediately.