Prepare the Chicken:
In a medium bowl, combine the cornstarch, flour, salt, and pepper. Add the chicken pieces to the bowl and toss them in the flour mixture until fully coated. Shake off any excess flour.
- Fry the Chicken:
Heat the vegetable oil in a large skillet or wok over medium-high heat. Once the oil is hot, add the chicken in batches, ensuring not to overcrowd the pan. Fry the chicken for about 5-6 minutes, or until golden brown and crispy. Remove from the skillet and drain on a paper towel-lined plate. Continue frying the remaining chicken.
- Make the Mongolian Sauce:
In a small bowl, whisk together the soy sauce, brown sugar, hoisin sauce, rice vinegar, garlic, ginger, and red pepper flakes (if using). Pour the sauce into the skillet and bring it to a simmer over medium heat. Cook for 2-3 minutes, stirring occasionally.
- Thicken the Sauce:
Stir in the cornstarch-water mixture and cook for another 1-2 minutes, until the sauce thickens and becomes glossy.
- Combine Chicken and Sauce:
Add the fried chicken back into the skillet with the sauce and toss to coat evenly. Continue cooking for 1-2 minutes to ensure everything is well combined and heated through.
- Garnish and Serve:
Remove from heat and garnish with sliced green onions and sesame seeds, if desired. Serve over steamed rice, noodles, or with your favorite side dishes.