Place water and dried kombu in a pot and let it sit for 30 minutes. Heat on low and remove kombu just before boiling. Transfer to a heatproof bowl to make kombu broth.

Tear konjac into bite-sized pieces using a spoon. Add konjac and enough water to cover it to the pot. Boil on medium heat for 3 minutes, then drain and set aside.

Wipe excess oil from fried tofu with a paper towel. Cut tofu into strips. Slice carrot into half-moons and burdock root into thin diagonal slices. Soak burdock in water and drain.

Heat sesame oil in the cleaned pot over medium heat. Stir-fry konjac until coated with oil. Add tofu, carrot, and burdock, and stir-fry until well combined. Pour kombu broth and bring to a boil. Cover and simmer on low heat for 8 minutes until vegetables are tender. Stir in miso and heat briefly.