Cut the vegetables into bite-sized pieces. Soak the cut burdock in water for a few minutes and drain. Cut the pork into bite-sized pieces.
Heat the sesame oil in a large pot, add the ginger, then fry the pork until no longer pink.
Add all the vegetables (and fried tofu, if using) and stir-fry for 1 to 2 minutes to coat them in the oil.
Add the water and bring to a boil. Skim off the foam, add the dashi granules, and simmer for 10 to 15 minutes until the taro and daikon are tender.
Reduce the heat to low and dissolve about two-thirds of the miso. Taste and add more until it tastes right. Do not boil hard after adding the miso.
Serve in large bowls topped with chopped green onion.