Cook the chicken: Begin by placing the chicken pieces in a mixing bowl. Add the cornstarch and pepper. Toss everything together until the chicken is thoroughly coated. This coating helps create a crispy exterior. In a large skillet or wok, heat the sesame oil over medium-high heat. Once hot, add the chicken in batches if your pan isn’t large enough to avoid overcrowding. Cook until the pieces are golden brown and cooked through, about 5 to 7 minutes. Remove the chicken from the pan and set it aside.
Cook the veggies: If necessary, add a splash more of sesame oil to the pan. Then, add the sliced carrot, celery, red bell pepper, broccoli, red onion, and dried chilies. Sauté the vegetables, stirring occasionally, for around 4 to 5 minutes until they soften but remain crisp. The colors should be vibrant and the aromas should be delightful.
Make the Hunan sauce: In a separate bowl, whisk together the soy sauce, chicken broth, oyster sauce, honey, rice vinegar, and additional cornstarch. This mixture is where all the magic happens, bringing together all the flavors.
Incorporate the sauce: Add the minced garlic and ginger to the vegan stir-fry. Sauté for 30 seconds until fragrant, then pour the prepared sauce into the skillet. Reduce the heat to medium, stirring constantly until the sauce thickens, about 2 to 3 minutes. The sauce should be glossy and coat the back of a spoon.
Finish: Finally, add the cooked chicken back into the skillet. Toss everything together to ensure the chicken is well coated in the sauce. Sprinkle chopped peanuts on top for added crunch and flavor. Serve immediately over rice or noodles.