Marinate the Chicken. In a bowl, combine the chicken pieces with soy sauce and cornstarch. Mix well and set aside to marinate for 10 minutes.
Prepare the Sauce. In a small bowl, whisk together the soy sauce, rice vinegar, hoisin sauce, sugar, chicken broth, and cornstarch until smooth. Set aside.
Stir-Fry the Chicken. Heat vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
Cook the Vegetables. In the same skillet, add more oil if needed. Add the dried red chilies, garlic, and ginger. Stir-fry for 1-2 minutes until fragrant. Add the bell peppers and green onions, and stir-fry for another 2-3 minutes.
Combine and Cook. Return the chicken to the skillet and pour in the prepared sauce. Stir well to coat everything evenly. Add the peanuts and cook for another 2-3 minutes until the sauce thickens and everything is heated through.
Serve. Serve your Kung Pao Chicken hot over a bed of steamed rice.