In a large bowl, toss the chicken with 2 tablespoons of cornstarch, salt, and white pepper. Add 1 tablespoon of vegetable oil, and toss again (this will help separate the chicken strips so they don’t clump up together).
In a wok or a 12-inch pan, heat 2 tablespoons of vegetable oil over medium-high heat. Add the chicken, spreading it in a single layer, and cook for 30 seconds per side. Remove to a plate and set aside (the chicken won’t be fully cooked and does not need to be browned).
Add carrots, snow peas, and mushrooms to the same pan. Stir and cook for 3 minutes, or until they just start to soften.
Add water chestnuts, bamboo shoots, and garlic, and saute for one minute.
Return the chicken to the skillet. Pour in the chicken stock, and soy sauce, and add sugar and sesame oil. Bring the mixture to a gentle boil and cook for 1-2 minutes.
Mix 1 tablespoon of cornstarch with 1 tablespoon of cold water to make a slurry for thickening the sauce. Pour the slurry over the sauce, stir, and cook for 1 minute. The sauce should thicken enough, but if it does not, add more cornstarch slurry.
Taste the sauce for seasoning and adjust if needed (salt). Remove from heat, garnish with toasted sesame seeds if desired, and serve over rice.