In a large mixing bowl, combine the low-sodium soy sauce, honey, cold water, ground ginger, garlic powder, and sesame oil. Whisk together until well blended. If you prefer a sweeter sauce, feel free to add an additional 1/4 cup of honey.
Add the cubed chicken breasts to the bowl with the sauce. Stir well to coat the chicken evenly. Cover the bowl and let it marinate for at least 30 minutes in the refrigerator.
Preheat your oven to 375°F (190°C).
In a large skillet over medium heat, add a splash of oil if needed and sauté the diced yellow onion, minced garlic, and fresh ginger until fragrant, about 3–4 minutes. Then, add the broccoli florets, shredded carrots, and snow peas. Cook for an additional 5 minutes until the vegetables are just tender but still vibrant in color.
In your baking dish, combine the marinated chicken (along with the marinade) and the sautéed vegetables. Stir everything together to distribute the chicken and veggies evenly.
Cover the baking dish with aluminum foil and bake in the preheated oven for 25 minutes. Then, uncover and bake for an additional 15 minutes.
While the chicken bake is cooking, prepare your brown rice according to package instructions. Once the Teriyaki Chicken Bake is done, serve it over a generous scoop of brown rice.