Soak black mushrooms in 1 cup hot water 15 minutes; drain, reserving 1/4 cup mushroom liquid. Chop mushrooms, and set aside.
Cut chicken into 1/2-inch-thick strips; toss with 1 tablespoon cornstarch and 2 tablespoons soy sauce. Set aside.
Stir together remaining 2 tablespoons soy sauce, reserved 1/4 cup mushroom liquid, black beans, and next 3 ingredients with a fork, pressing to mash.
Heat 2 tablespoons oil in a large skillet or wok over medium-high heat 2 minutes. Add chicken, and stir-fry 5 minutes or until done. Remove from skillet.
Heat remaining 2 tablespoons oil in skillet over medium-high heat 2 minutes.
Add onion, and stir-fry 1 minute and 30 seconds; add garlic, and stir-fry 30 seconds. Add mushrooms, and stir-fry 1 minute. Add chicken and cabbage, and stir-fry 30 seconds. Make a well in center of mixture.
Stir together remaining 1 tablespoon cornstarch and 2 tablespoons water until smooth. Add cornstarch mixture and bean mixture to skillet, and bring to a boil; boil 1 minute or until thickened.
*1 tablespoon hoisin sauce may be substituted for oyster sauce.