In a medium-sized bowl, combine the egg white and 2 tablespoons of cornstarch. Stir until fully combined. Add the cubed chicken to the bowl and season with a sprinkle of salt and pepper.
Heat a wok (or large skillet) over medium-high heat with 1 tablespoon of olive oil and 1 tablespoon of sesame oil. Allow the excess egg mixture to drip off the chicken before adding it to the hot wok. Stir the chicken every 2-3 minutes, browning it on each side until it is cooked through, for about 8-10 minutes in total.
While the chicken is cooking, in a small bowl, combine the water, brown sugar, soy sauce, hoisin sauce, ketchup, parsley, chili peppers (or flakes), and the remaining 2 tablespoons of cornstarch. Whisk together until well blended.
Chop the broccoli and cubanelle pepper, and peel and slice the ginger. Add them to the wok along with 1 tablespoon of sesame oil, stirring gently to coat the vegetables. Cook for approximately 2-3 minutes, then pour the sauce into the wok.
Bring the sauce to a boil, then reduce the heat and simmer, stirring occasionally, until the broccoli is tender and cooked, for about 2 more minutes. Remove from heat completely. The sauce will thicken as it cools. Serve the General Tso's Chicken alongside rice and enjoy!