Heat 1 tablespoon oil in a wok over high heat until it begins to smoke. Stir in broccoli and fresh mushrooms, then add straw mushrooms, bamboo shoots, and water chestnuts. Stir-fry until broccoli is tender and all vegetables are hot, about 5 minutes. Transfer to a bowl and wipe out the wok.

Heat remaining 1 tablespoon oil in the wok over high heat until it begins to smoke. Add garlic and stir-fry until it turns golden, a few seconds. Add chicken and stir-fry until browned on the edges and no longer pink in the center, about 5 minutes.

Stir broth, cornstarch, sugar, soy sauce, oyster sauce, and rice wine together in a small bowl; pour over chicken in the wok and bring to a boil, stirring constantly. Boil until sauce thickens and is no longer cloudy, about 30 seconds. Return vegetables to the wok; toss with sauce and cook until heated through, about 1 minute.