Heat 2 tablespoons sesame oil in a large pot over medium-high heat.
Add the bok choy and cook it for about 4 minutes, stirring frequently, until it's softened. Remove it from the pot and set it aside on a plate.
If your pot is dry add another tablespoon of sesame oil. Add in your mushrooms, shallots, garlic, and ginger. Cook it for about 2 minutes, just until it becomes fragrant.
Stir in the broth, cover, and bring it to a boil. Reduce the heat to low and let the broth come to a gentle simmer.
While your broth is heating up, cook your noodles in a separate pot according to the packaging directions. My noodles required 3 minutes of boiling, then a rinse with cold water. I drizzle mine with the remaining tablespoon of sesame oil and give them a gentle toss to avoid having the noodles stick together.
Once your noodles are cooked and your broth is simmering, add your bok choy, tamari, and rice vinegar to the broth.
Add some noodles to your serving bowls (about 3 oz per serving). Ladle the broth over your noodles and garnish with chopped green onions, sesame seeds, and red pepper flakes.