Make the Soup Base:In a small bowl, soak dried shiitake mushrooms and kombu in 4 cups of water. Set aside for 4–6 hours, or preferably overnight, to extract the deep umami flavor.
Prepare the Vegetables:Peel the Japanese sweet potato and slice it into ¼-inch (about 5 mm) thick half-moon pieces.Remove the soaked shiitake from the water and gently squeeze out the excess liquid. Trim off the stems and thinly slice the caps (about 5 mm thick).Slice the burdock root diagonally into thin pieces, or use the sasagaki style (shaving it into thin curls).
Stir-Fry the Vegetables:In a medium pot, heat 1 tablespoon roasted sesame oil over medium heat. Add the burdock, sweet potato, and shiitake, then stir-fry until the burdock becomes aromatic.
Simmer the Soup:Pour the shiitake and kombu soaking liquid into the pot.Just before it comes to a full boil, remove the kombu.Skim off any foam that rises to the surface, lower the heat, and simmer until the sweet potato and burdock become tender (about 7–8 minutes).
Add the Miso:Turn off the heat. In a ladle, dissolve 3 tablespoon miso with a small amount of soup, then stir it back into the pot.Gently mix — do not boil after adding miso to keep its mellow, delicate flavor.
Serve:Ladle the soup into bowls and serve warm. Optionally, sprinkle chopped green onion or a touch of sesame oil on top before serving for extra aroma.