Bring a large saucepan of water to a boil. In a small bowl, combine the chicken broth with the soy sauce, oyster sauce, sesame oil and the 1 teaspoon of chile sauce.
Add the pasta to the boiling water and cook until just al dente, 2 to 3 minutes (or according to package directions). Drain.
In a large nonstick skillet, heat the vegetable oil. Add the mushrooms and cook over high heat, stirring occasionally, until tender and browned, about 5 minutes.
Add the ginger and garlic and cook until fragrant, about 1 minute.
Add the snow peas and broccoli and cook, stirring and tossing occasionally, until the snow peas are barely cooked, about 2 minutes.
Stir in the noodles and the sauce along with the scallions. Cook, stirring occasionally, until the sauce is absorbed and the noodles are browned in spots, about 5 minutes.
Serve immediately.
