Heat 2 tablespoons vegetable oil in a large pot. Add in the shiitake mushrooms and cook,  stirring frequently,  until softened, 4-5 minutes. Transfer mushrooms onto a plate, cover with aluminum foil (to keep them warm), and set aside. Do not wash the pot.

To make the miso broth: Heat the remaining 1 tablespoon oil in the now-empty pot. Add in the white parts of the green onions, ginger, and garlic. Cook, stirring constantly, for 2 minutes.Pour in the vegetable stock. Bring it to a boil.

Meanwhile, place miso paste into a bowl. Ladle ½ cup of the boiling liquid and whisk until miso is completely dissolved. Add the mixture back into the pot along with tamari (or soy sauce) and sesame oil.

To cook the eggs and noodles: Fill a large pot with water and bring it to a boil.

Lower eggs into the pot and cook them for 8 minutes. Using a slotted spoon remove them from the pot and place them into a bowl of ice water and set aside.

Bring the water back to a boil.

Add the noodles and bok choy and cook them until they are al-dente and bok choy turned bright green (and softened), 3-4 minutes. Drain.

In the meantime, peel the eggs and halve them lengthwise.

To assemble: Place noodles and bok choy in a bowl, pour some miso stock over it and top it off with shiitake mushrooms and eggs. Garnish with the reserved green parts of the scallions and sesame seeds.