Cut chicken breast crosswise into thin slices about 1/4" thick. In a bowl, toss chicken with cornstarch, sherry, salt and pepper to coat evenly. Let stand 10-15 minutes. Meanwhile, cut broccoli florets from stems. Peel and cut stems into 2" pieces about 1/2" thick. In a large saucepan of boiling, salted water, cook broccoli stems and florets until broccoli is a bright green and crisp-tender, about 3 minutes. Drain and rinse under cold running water; drain well. In a wok, heat oil over high heat until just smoking. Add garlic and ginger and stir fry until aromatic, about 30 seconds. Add chicken and stir fry until chicken becomes white and opaque, 3-5 minutes. Add water chestnuts, broccoli, soy sauce, oyster sauce, chicken broth, and sugar. Stir fry until vegetables are tender and heated through, about 3 minutes. Serve.