Heat 1 tablespoon of vegetable oil in a wok or large skillet over high heat until it begins to smoke. Stir in the fresh mushrooms, broccoli, bamboo shoots, water chestnuts, and straw mushrooms. Cook and stir until all the vegetables are hot, and the broccoli is tender, about 5 minutes. Remove from the wok, and set aside. Wipe out the wok.
Heat the remaining tablespoon of vegetable in the wok until it begins to smoke. Stir in the garlic, and cook for a few seconds until it turns golden-brown. Add the chicken, and cook until the chicken has lightly browned on the edges, and is no longer pink in the center, about 5 minutes. Stir together the cornstarch, sugar, soy sauce, oyster sauce, rice wine, and chicken broth in a small bowl. Pour over the chicken, and bring to a boil, stirring constantly. Boil for about 30 seconds until the sauce thickens and is no longer cloudy. Return the vegetables to the wok, and toss with the sauce.