In a bowl, toss the Chicken with the Marinade ingredients and 1 tbsp cornstarch. Let marinate for at least 15 minutes.
In a separate bowl, whisk together all Sauce ingredients.
Heat 1 tbsp Vegetable oil in a large skillet or wok over medium-high heat. Add the chicken and cook until browned and cooked through, about 6-8 minutes. Remove chicken and set aside.
Add the remaining 1 tbsp Vegetable oil and Sesame oil to the skillet. Add the Onion, Carrots, and Red bell pepper and stir-fry for 3-4 minutes until slightly softened.
Add the Broccoli and continue to stir-fry for another 2-3 minutes.
Pour the Sauce over the vegetables and bring to a simmer. Cook for 1-2 minutes, stirring constantly.
Stir in the cornstarch slurry and cook until the sauce thickens, about 1 minute.
Return the cooked chicken to the skillet and toss to coat with the sauce. Serve immediately.