Heat 1-2 tablespoons olive oil in a medium-sized stockpot over medium heat.
To the oil add the diced shallots and mix well. Cook over medium heat for 4-5 minutes, or until the shallots turn translucent and start to soften. Stir often.
Chop the end off of each green onion- dividing the white part from the green part. Chop and set aside the green part for topping. Meanwhile, finely chop the white part of each green onion.
Add the white part of the green onions, minced garlic, and ginger to the shallots and mix. Cook, stirring occasionally, for 1-2 minutes or until garlic and ginger is fragrant.
Carefully pour the chicken stock or water (or mix) into the pot and bring to a simmer. To the pot add the star anise and soy sauce. Cover and continue to simmer for 10 minutes.
Remove lid from the pot and carefully remove and discard each star anise from the soup.
Add the sliced mushrooms, uncooked noodles, and bok choy to the pot and simmer for 5-8 minutes, or until noodles and bok choy are tender. Season to taste.
Divide soup between bowls and garnish with sesame seeds, the green parts of green onions and red pepper flakes (if desired).