Thinly slice the daikon and carrot. Cut the potato and cabbage into bite-sized pieces and thinly slice the naganegi diagonally. Grate the ginger.
Heat the sesame oil in a large pot. Add the pork and black pepper, and sauté until the pork changes color.
Add the daikon, carrot, potato, cabbage, water, and dashi powder. Bring to a boil, then reduce the heat and simmer for about 20 minutes, or until the vegetables are tender. Skim off any foam occasionally.
Add in the grated ginger, naganegi, and miso. Simmer gently for another 2–3 minutes. Do not let the soup boil after adding the miso.
Serve hot with shichimi togarashi, if desired.