In a large skillet, heat the vegetable oil over medium-high heat. Add the chicken pieces and cook for about 5-7 minutes, stirring occasionally, until browned and cooked through.
While the chicken is cooking, steam the broccoli florets until tender, about 3-4 minutes. You can do this in a microwave or on the stovetop.
Once the chicken is cooked, pour the teriyaki sauce over the chicken and stir to coat evenly. Let it simmer for 2-3 minutes until the sauce thickens slightly.
Add the steamed broccoli, sliced bell peppers, and shredded carrots to the skillet. Stir everything together and cook for an additional 2-3 minutes until the vegetables are heated through.
To serve, place a scoop of cooked rice in a bowl, top with the teriyaki chicken and vegetable mixture, and garnish with sliced green onions and sesame seeds if desired.