Cook the jasmine rice according to package instructions, typically combining 1 cup of rice with 1.5 cups of water in a pot. Bring to a boil, then reduce heat to low, cover, and simmer for about 15 minutes.
Prepare the teriyaki sauce by whisking together soy sauce, honey, rice vinegar, garlic, ginger, cornstarch, and water in a small bowl until smooth.
In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the sliced chicken breast and stir-fry for about 5-7 minutes, or until the chicken is cooked through and no longer pink.
Add broccoli, bell pepper, and carrot to the skillet. Stir-fry for an additional 3-4 minutes until the vegetables are tender but still crisp.
Pour the teriyaki sauce over the cooked chicken and vegetables in the skillet. Stir well to coat everything evenly and continue cooking for another 2-3 minutes until the sauce has thickened.
Fluff the cooked rice with a fork and portion it into four bowls. Top each bowl with the teriyaki chicken and vegetable mixture.
Garnish each bowl with sesame seeds and sliced green onions.