Prepare the noodles according to the package directions.
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 using) and combine. Bring to a boil. Add the scallions, carrots, and green beans. Simmer until the vegetables are tender, 5 to 6 minutes.
Drain the noodles and cut into 3-inch lengths. Divide the noodles among individual bowls and ladle the soup over the top.
Tip: You can find cellophane and rice noodles in the Asian-food aisle of most supermarkets. If you prefer a more substantial soup, substitute 8 ounces of angel-hair pasta or whole-wheat spaghetti, breaking the strands into pieces before cooking.