Heat the oil, garlic and gingerroot in a wok or large skillet with a tightfitting lid over high heat until fragrant, 1 to 2 minutes.
Add chicken strips, onion, celery, bell pepper and green beans. Stir-fry for 4 minutes. Stir in mushrooms, carrots, zucchini and cabbage.
Reduce heat to low, cover and steam until tender, about 3 to 5 minutes. Stir in sesame oil and soy sauce. Serve hot and enjoy!