Prepare the noodles according to the package directions. Drain and cut into 3-inch lengths.
Meanwhile, heat the oil in a large saucepan over medium-high heat. Add the mushrooms and cook, stirring occasionally, for 2 minutes.
Add the broth, soy sauce, ginger, and chili sauce (if desired) and combine. Bring to a boil.
Add the scallions, carrots, and green beans. Simmer until the vegetables are tender, 5 to 6 minutes.
Divide the noodles among individual bowls and ladle the soup over the top.