In a small bowl, combine soy sauce, water, and sesame oil. Add sugar, cornstarch, and pepper and stir until blended. Set aside.
Over high heat, heat a wide, heavy-bottomed pan or wok. Add canola oil and swirl to coat bottom and sides of the pan. Heat until hot but not smoking.
Add green beans and spread in a single layer on the bottom of the pan. Stir-fry for about 2 to 4 minutes or until half done.
Add mushrooms, onions, and garlic. Cook, stirring regularly until vegetables are tender yet crisp.
Stir sauce mixture to redistribute cornstarch and add to pan. Cook, stirring regularly until thickened.
Transfer to serving plate and garnish with sesame seeds if desired. Serve hot.