Place the meat down on a chopping board using the palm of your hand and slice horizontally into very thin long strips, then cut the strips crosswise into stamp-size pieces. Set pork aside.
With a potato peeler, peel the burdock, if using, then cut diagonally into 1/2-inch thick slices. Quickly plunge the slices into a bowl of cold water to prevent them from discoloring. If using parsnip, peel, cut it in half lengthwise, then cut it into 1/2-inch thick half moon shaped slices.
Peel and slice the daikon into 2/3-inch thick disks. Cut the disks into 2/3-inch cubes. Remove the shiitake stalks and cut the caps into quarters.
Place the tofu in a pan of boiling water and cook for 1 minute. Drain and cool. Cut in quarters lengthwise, then crosswise into 1/8-inch thick pieces.
Heat some sesame oil in a heavy cast-iron pan, until smoking. Stir-fry the pork, then add the tofu and all the vegetables except for the scallions. When the color of meat has changed, add the stock.
Bring to boil over medium heat and skim off foam until the soup looks clear. Reduce the heat, cover and simmer for 15 minutes.
Put the miso in a small bowl and mix with 4 tablespoons hot stock to make a smooth paste. Stir one-third of the miso into the soup. Add the scallions and remove from heat.
Serve hot in individual bowls, sprinkle with sesame seeds.