1. Rinse the mushrooms in cold water; drain. Remove and discard the stems. Cut the caps into 1-inch strips. Wash the asparagus thoroughly. Break off the tough ends of the asparagus as far down as the stalk snaps easily. Mix together the cornstarch and cold water in a small bowl.
2. Heat a heavy nonstick pan or wok over high heat. Add the vegetable oil and rotate the pan to coat the sides. Add the garlic, asparagus and salt and stir-fry for 1 minute. Add the mushrooms and continue to stir-fry until mixed. Stir in the oyster sauce. Stir in the chicken broth and heat to boiling. Stir in the cornstarch mixture; cook and stir until thickened, about 30 seconds. Turn off the heat and remove the asparagus with tongs. Arrange the asparagus across a platter and top with mushrooms.