Clean and halve the baby bok choy. Slice the green onions, keeping the white and green parts separate. Clean and slice the shiitake mushrooms.
In a large pot, heat the sesame oil over medium heat. Add the white parts of the green onions, garlic, and ginger. Sauté until fragrant.
Add the shiitake mushrooms and cook for about 3 minutes until they start to soften.
Add the bok choy and sauté until it starts to wilt.
Pour in the broth and soy sauce. Bring the mixture to a simmer and cook for about 5 minutes.
Add the noodles to the pot and cook according to the package instructions until tender.
Soft Boiled Eggs (Optional):a. In a separate pot, bring water to a boil. Gently lower the eggs into the water and boil for about 46-7 minutes for a soft yolk.b. Remove the eggs from the water and place them in ice-cold water to stop the cooking process. Peel the eggs carefully. Ladle the soup into bowls. Add halved soft-boiled eggs on top if using. Garnish with the green parts of the green onions and some sesame seeds. If you like your soup spicy, add a dash of chili oil or some fresh chili.