In a bowl, combine chicken, flour, sesame oil, egg white, salt, and pepper. Toss to coat.
Heat a wok or wide pan with oil. Add the chicken, cook for 2-3 minutes on each side or until they browned. When the chicken is cooked through, remove them from the pan, and transfer them to a platter with a paper towel to drain excess oil. Set aside.
Combine all the sauce ingredients, mix until well incorporated or when the corn starch is dissolved. Set aside.
Heat 3 tablespoons of oil into a clean pan, add the garlic and onion, saute for a couple of minutes or until the onion is tender. Season with red chili pepper flakes or ground pepper.
Add shiitake mushrooms, saute for a couple of minutes or until tender. Add the peppers, stir to combine, saute for another minute or until tender.
Add the cooked chicken back to the pan, stir to combine. Mix the sauce to make sure there are no lumps, then add to the pan, stir to combine. Sprinkle the green onions, keep stirring until the sauce thickened. Sprinkle toasted sesame seeds.