Place the sliced chicken breast into a bowl or resealable plastic bag. Add cornstarch, salt, and pepper, tossing or shaking until each piece is evenly coated.
Heat the vegetable oil in a large wok or skillet over medium-high heat. Add the chicken and cook, stirring frequently, until lightly browned on all sides. Remove the chicken from the pan and set aside, allowing it to finish cooking later with the vegetables.
In the same pan, add the red bell pepper and broccoli florets. If necessary, drizzle in a little more oil. Stir-fry for 3–5 minutes, or until the vegetables are tender-crisp.
In a separate bowl, combine the vegetable broth, Shaoxing wine, soy sauce, chili paste, garlic, ginger, honey, and cornstarch. Whisk until the mixture is smooth and fully blended.
Return the chicken to the pan with the vegetables. Pour in the prepared sauce, stirring continuously until it thickens and the chicken is cooked through.
Remove from heat. Garnish with sesame seeds or finely sliced green onions, if desired. Serve promptly with steamed rice, noodles, or enjoy as a stand-alone dish.