In a bowl, combine chicken pieces, 2 tablespoons of soy sauce, and cornstarch. Mix well and let it marinate for 10 minutes.

In a separate bowl, whisk together 1/2 cup soy sauce, brown sugar, rice vinegar, garlic, ginger, and sesame oil until well combined.

Heat vegetable oil in a large skillet over medium-high heat. Add the marinated chicken and cook until browned and cooked through, about 5-7 minutes.

Add bell pepper, broccoli, and carrots to the skillet. Stir-fry for an additional 3-5 minutes until vegetables are tender-crisp.

Pour the prepared sauce over the chicken and vegetables. Stir well to coat and cook for another 2-3 minutes until the sauce thickens slightly.

Remove from heat, garnish with green onions and sesame seeds, and serve hot over rice or noodles.