Cook the rice according to the package instructions and set it aside.
In a large skillet or wok, heat the vegetable oil over medium-high heat.
Add the chicken pieces to the skillet and cook for about 5-7 minutes, or until browned and cooked through, stirring occasionally.
Add the minced garlic and ginger to the chicken and cook for an additional minute until fragrant.
Add the broccoli, bell pepper, and snap peas to the skillet. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
In a mixing bowl, combine the soy sauce, honey, sesame oil, and cornstarch mixture. Stir well.
Pour the sauce mixture over the chicken and vegetables in the skillet. Cook for an additional 2-3 minutes, stirring constantly, until the sauce thickens and coats the chicken and vegetables.
To serve, place a scoop of rice in each bowl and top with the sesame chicken and vegetable stir-fry.
Garnish with sesame seeds and sliced green onions, if desired.