Soak mushrooms in warm water until soft, about 30 minutes; drain.
Remove and discard stems; slice caps.
Rinse bean sprouts in cold water; drain.
Heat oil in wok or skillet until hot.
Add mushrooms, bean sprouts, garlic and ginger root; stir-fry 2 minutes.
Stir in 1/2 cup water; heat to boiling.
Mix 1 tablespoon water, the soy sauce and cornstarch; stir into vegetable mixture.
Cook and stir until thickened, about 20 seconds.
Garnish with green onions.