Preheat the oven to 350°F (175°C). Spray a 9×13 baking dish with non-stick cooking spray.
In a saucepan over medium-high heat, combine soy sauce, ½ cup water, honey, ground ginger, and minced garlic. Bring to a boil and cook for 1 minute.
In a small bowl, mix cornstarch with 2 tbsp of water to create a slurry. Stir it into the saucepan and cook, stirring constantly, until the sauce thickens.
Place chicken breasts in the prepared baking dish. Arrange broccoli, carrots, and snow peas around the chicken. Pour 1 cup of teriyaki sauce over the contents.
Cover with foil and bake for 30 minutes or until the chicken is cooked through.
Remove the casserole from the oven. Shred the chicken directly in the baking dish using two forks.
Stir in the cooked white rice and pour in the remaining sauce. Mix everything to combine evenly.
Return to the oven, uncovered, and bake for another 10 minutes.
Let the casserole rest for 5 minutes before serving. Optionally drizzle with extra sauce or garnish with sesame seeds or chopped scallions.