Cut the broccoli, bell peppers, and carrots into bite-sized pieces. Slice the green onions, keeping the white portions separate from the green tops since they will be used at different stages of cooking.
Cut the chicken into small, even pieces and season lightly with salt and pepper.
Heat the sesame oil in a large skillet over medium heat. Add the garlic, the white parts of the green onions, and the chicken. Cook, stirring frequently, until the chicken is lightly browned on the outside and almost fully cooked. Transfer the chicken mixture to a plate and set aside.
Add the broccoli, bell peppers, and carrots to the same skillet. Cook for 5-7 minutes, stirring occasionally, until the vegetables begin to soften but still have a little crunch. Add a small amount of extra oil if the pan seems dry.
While the vegetables cook, whisk together the teriyaki sauce and honey in a small bowl.
In a separate bowl, combine the cornstarch and water, stirring until smooth. Pour the cornstarch mixture into the teriyaki sauce and whisk until fully blended.
Return the chicken mixture to the skillet with the vegetables. Pour the sauce over everything and stir to combine. Let the mixture simmer for a few minutes, stirring occasionally, until the sauce thickens and coats the chicken and vegetables.
Spoon the teriyaki chicken and vegetables over rice and garnish with the sliced green onion tops. Serve warm and enjoy!