In a small bowl, combine beef, 4 tablespoons of the soy sauce, and cornstarch. Stir to fully coat meat and let stand for about 10 to 15 minutes.
In another bowl, combine water, oyster sauce, the remaining 2 tablespoons soy sauce, Chinese cooking wine, sugar and pepper. Stir until well blended and set aside.
With hands, gently squeeze meat to extract marinade. Add excess liquid into the bowl of oyster sauce mixture (this is important as the cornstarch from the marinade will thicken the stir-fry sauce).
In a wok or wide pan over high heat, heat 1 tablespoon of the oil. Add bell peppers, baby corn, and water chestnuts and cook for about 30 seconds.
Add snow peas and cook for another 10 seconds. Remove from pan and keep warm.
Add 1 tablespoon of oil to the pan. Add beef in a single layer and cook for about 3 to 4 minutes per side. Do not overcrowd the pan, cook beef in batches if needed. Remove from pan and set aside.
Wipe down wok as needed. Add the remaining 1 tablespoon oil. Add onions and garlic and cook until softened.
Add beef and vegetable mixture. Continue to cook, stirring occasionally, for about 2 to 3 minutes or until heated through and coated with sauce. Serve hot.