Preheat a soup pot or large/deep saute pan over medium heat. Add the oil, if using, and bok choy and cook undisturbed for 1 minute. Stir and cook for another minute, or until dark green, wilted, and slightly seared. Transfer bok choy to a plate.
Add the shallots and mushrooms to the pot. Stirring occasionally, cook 3 to 5 minutes or until softened. Add the garlic and ginger, and cook for another 2 to 3 minutes.
Add the water, soy sauce, and star anise. Bring to a boil. Reduce heat to a simmer and cook 10 minutes.
Add the noodles to the pot and cook according to package directions (increase heat to maintain a simmer). Once noodles are tender, return bok choy to the pot. Remove the star anise before serving.
Garnish with sliced green onion and serve.
Nutrition content will vary depending on type and brand of noodles used.