Add cubed chicken to a medium bowl, add soy sauce, honey, garlic, ginger, lime juice, and sesame oil. Let marinate for 20 minutes.
Meanwhile, combine brown rice and water in a small saucepan over medium-high heat. Bring to a boil, reduce heat, and let simmer, covered, for 15-20 minutes.
Add broccoli, cauliflower, and carrots to the pot, cover and cook for an additional 5 minutes or until vegetables are tender and the rice is fully cooked.
Heat a nonstick frying pan over medium heat. Add the chicken, reserving the marinade.
Cook for 4-5 minutes, stirring occasionally, until the chicken is no longer pink. Pour in remaining marinade, and cook for an additional 4-5 minutes, or until sauce has thickened. Add the sesame seeds.