Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken and cook until lightly browned and cooked through. Remove and set aside.
In the same skillet, add the remaining oil and stir-fry the broccoli, bell pepper, and carrot for 4-5 minutes until tender-crisp.
Add the garlic and cook for an additional minute.
In a small bowl, whisk together soy sauce, honey, and cornstarch mixture. Pour over the vegetables.
Return the chicken to the skillet and toss to combine, cooking for another 2-3 minutes until the sauce thickens.
Serve hot over cooked rice.