Coat the Chicken: Place the chicken pieces in a bowl and toss them with ⅓ cup cornstarch until each piece is evenly coated.
Cook the Chicken: Heat 2-3 tablespoons of vegetable oil in a large pan or wok over medium-high heat. When the oil reaches the right temperature, place the chicken pieces in the pan in a single, even layer. Fry them for about 5-6 minutes, flipping halfway through, until they are golden and cooked through.
Sauté the Onion: In the same pan, add the onion wedges and stir-fry for 2-3 minutes until they start to soften but still retain some crunch. Set the onions aside with the chicken.
Make the Sauce: In a small bowl, mix 1 tablespoon of cornstarch with ¼ cup of chicken broth or water until smooth. In the same pan, reduce the heat to medium and add sesame oil, grated ginger, and minced garlic.
Build the Sauce: Stir in the rice vinegar, soy sauce, and brown sugar, allowing the sauce to simmer for 2-3 minutes until the sugar dissolves. Pour the cornstarch blend into the skillet, whisking continuously to ensure a smooth consistency without any clumps. Let the sauce simmer for another 2 minutes until it thickens.
Combine Chicken and Sauce: Return the cooked chicken and onions to the pan, tossing them with the sauce until everything is evenly coated. Add red pepper flakes if using and green onions. Stir for an additional 1-2 minutes to heat everything through.
Serve: Serve the Mongolian Chicken over steamed rice or alongside stir-fried vegetables for a complete meal.