Cut veggies into chunks and minces garlic. Set aside for later.
Combine all the sauce ingredients into a bowl and whisk together. Set aside. (I recommend doing this ahead of time so the flavors can get happy together).
Dice chicken into manageable chunks; about 1/4-1/2 inch pieces.
Beat the egg and add cayenne pepper. Combine chicken into the egg mixture. Combine flour and corn starch in a ziplock bag, add the chicken pieces from the egg mixture into the bag. Close and shake. Shake off excess flour for the cooking process.
Begin cooking chicken in a wok with about 2 inches of peanut oil in it. The oil should be 375-400 degrees. Work in small batches. Don't overload the wok.
Once all the chicken is cooked, reserve only about 3 tablespoons of the oil in the bottom of the wok. Crank the heat up high and add your chicken back into the wok. Cook until all the pieces get a nice golden brown. You can add your veggies during this process.
Once your veggies are cooked the way you like them add the sauce mixture and stir constantly. Saute for 3 minutes or so, allowing the sauce to thicken.