In a medium pot, combine 2 cups of brown rice with 3 ½ cups of water. Bring to a boil, then reduce heat to low, cover, and simmer for about 40-45 minutes, or until the rice is tender and the water is absorbed. Once done, remove from heat and let it sit covered for an additional 10 minutes.
While the rice is cooking, heat the sesame oil in a large skillet over medium-high heat. Add the chicken chunks and cook for about 5-7 minutes, stirring occasionally, until the chicken is browned and cooked through.
Once the chicken is cooked, pour in the teriyaki sauce and low-sodium soy sauce. Stir to coat the chicken evenly and let it simmer for an additional 2-3 minutes to allow the flavors to meld.
Add the shredded carrots, chopped green onions, snow peas, and broccoli florets to the skillet. Sauté for another 3-5 minutes, or until the vegetables are tender but still vibrant and crisp.
To serve, scoop a generous portion of the cooked brown rice into bowls. Top with the chicken and vegetable mixture, ensuring you get a good balance of both. Drizzle with extra teriyaki sauce if desired, and garnish with additional green onions for a pop of color.