In a large skillet or wok, heat vegetable oil over medium-high heat.
Add the sliced chicken and season with salt and pepper. Cook until the chicken is browned and cooked through, about 5-7 minutes.
Remove the chicken from the skillet and set aside.
In the same skillet, add broccoli and bell pepper, stir-frying for about 3-4 minutes until they are tender-crisp.
Add minced garlic and stir-fry for an additional minute until fragrant.
In a small bowl, whisk together soy sauce, honey (or brown sugar), and sesame oil.
Pour the sauce over the chicken and vegetables in the skillet.
If you prefer a thicker sauce, add the cornstarch mixture and stir well to combine.
Cook for another 2-3 minutes until everything is heated through and the sauce has thickened slightly.
Serve hot, garnished with sesame seeds and sliced green onions if desired.
