Traditional Japanese Vegetable Soup (Kenchin Jiru)

Pour 500 ml water into a container and add 5 g dried kelp (kombu) and 10 g dried shiitake mushroom. Cover and allow to soak for at least 30 minutes, or overnight in the fridge for a deeper flavor.
Once rehydrated, remove the shiitake mushroom and thinly slice it. We will use it in the soup later.
Peel and slice 75 g carrot, 250 g daikon radish and 100 g burdock root (gobo). Slice the 20 g fried tofu pouch (aburaage) and roughly cut 150 g konjac (konnyaku). Cut the roots off of 100 g enoki mushrooms and cut 50 g Japanese leek (naganegi) into thin diagonal slices.
Pour the dashi and kombu into a small pot and heat over medium until almost boiling. When small bubbles start to appear around the edges, turn off the heat and remove the kombu (discard or save for another recipe).
Heat up another large pot on medium and add 1 tsp toasted sesame oil. Add all of the ingredients except for green onion (we'll add that later) and stir fry for a few minutes until lightly coated in oil. Add more oil if needed.
Pour the dashi into the large pot and simmer until the carrot and daikon are soft enough to pierce with a fork.
Add 2 tbsp sake, 2 tbsp mirin and 3 tbsp Japanese soy sauce (koikuchi shoyu) and let it boil for 1-2 minutes.
Finally add 50 g Japanese leek (naganegi) and simmer a few more minutes until softened to your liking. Taste test, simmer for longer for a more concentrated flavor or add a little more soy sauce if needed. Enjoy!