Heat sesame oil in a large pot over medium heat. Add mushrooms and cook until mushrooms start to soften, about 3 minutes. Add ginger and garlic and cook for 1 minute more.
Add stock and soy sauce to pot and increase heat to bring to a boil.
Add noodles and cook according to package instructions until al dente, which should be just a few minutes. Be careful not to overcook noodles.
Stir in cooked chicken and scallions. Taste and add salt if desired.
Serve immediately, adding toasted sesame seeds on top.