Cook noodles according to package; drain and set aside.
Combine broth, sake or rice wine, soy sauce, cornstarch, sugar and sesame oil in a small bowl. Set aside.
Heat wok or large skillet over medium high heat. Swirl in 2 teaspoons of oil, then add the beef. Stir-fry until cooked through, 3-4 minutes; remove from pan.
In the same skillet add the rest of the oil, then the mushrooms, scallions and garlic. Stir-fry until softened, about 3 minutes. Add the broth mixture and cook, stirring constantly, until the mix boils and thickens, about 2 minutes.
Stir in the beef and noodles. Cook, tossing frequently, until heated through, about 1 minute.