Combine the steak, soy sauce, and garlic in a small bowl and set aside. Drain the mushrooms, reserving 2/3 cup of the soaking liquid. Discard the stems and thinly slice the caps. In a small bowl, combine the reserved mushroom soaking liquid and the black bean sauce, wine, cornstarch, and chile sauce. Stir to dissolve the cornstarch and set aside. Heat 1 Tbs. of the vegetable oil in a 12-inch skillet over high heat. Add the beef and its marinade, and stir-fry until the meat is just browned, 45 to 50 seconds. Transfer the beef to a small bowl. Wipe out the skillet and heat the remaining 1 Tbs. oil over medium-high heat. Add the ginger and stir-fry until fragrant, 15 seconds. Add the broccoli and 1/4 cup water, cover, and steam until the broccoli is just tender, 3 to 5 minutes. Stir in the black bean sauce mixture, the stir-fried beef and the mushrooms and cook until the sauce is thick and bubbly, about 1 minute. Add the cashews and toss to combine. Serve with steamed rice.