Slice chicken into thin slices. (You can freeze the chicken for about 30 minutes to firm it up for easy slicing.)
In a medium bowl, whisk together the rice vinegar, cornstarch, soy sauce, and egg white.
Add the sliced chicken and toss several times to coat.
Cover and marinate for 20 minutes in the fridge. (Meanwhile, prepare the rest of the ingredients).
Combine Hunan Sauce ingredients in a medium bowl and whisk until the cornstarch dissolves. Set aside. (This recipe uses 2 teaspoons of chili bean paste for medium spiciness. You can start with 1 teaspoon if you prefer less heat and gradually add more.)
Place a wok or large pan over medium-high heat and add 1 tablespoon oil.
When hot, add the marinated chicken and fry for 3-4 minutes until the edges are lightly browned (the chicken is not fully cooked yet and will be cooked more later). Remove from the pan and set aside.
Lower the heat to medium. In the same wok/pan, add remaining oil. Stir in garlic and ginger and fry for 30 seconds or until fragrant.
Add broccoli, carrots, and red bell pepper. Stir fry for about 3 minutes until barely tender.
Give the prepared sauce a quick stir and pour into the pan.
Add back the par-cooked chicken and bring the sauce to a boil while stirring.
Stir fry until the chicken is evenly coated and the sauce has thickened (about 2-3 minutes).
Serve immediately with rice.