Whisk an egg white with cornstarch and soy sauce and add the chicken. Toss to coat and marinate for 30 minutes in the refrigerator.
Meanwhile, whisk the ingredients for the sauce together until the sugar and cornstarch are dissolved and set aside.
Heat a bit of oil in a large skillet over high heat. Add the chicken and saute until just browned. Remove from pan.
Using the same pan, add the mushrooms and saute for 2 minutes, then add in the carrot and snow peas and stir fry until crisp-tender
Add the chicken back to pan, along with the reserved sauce and simmer until thickened. Turn off the heat and stir in the bamboo shoots.