In a bowl, whisk together soy sauce, honey, rice vinegar, sesame oil, ginger, and garlic. Place the chicken thighs in a resealable bag or shallow dish and pour the marinade over them. Seal and let marinate in the refrigerator for at least 30 minutes, or up to 2 hours for deeper flavor.
Rinse the jasmine rice under cold water until the water runs clear. In a saucepan, combine the rice and water (or chicken broth) and bring to a boil. Once boiling, reduce heat to low, cover, and simmer for about 15 minutes or until the rice is cooked and water is absorbed. Remove from heat and let it sit covered for another 10 minutes.
In a small saucepan, combine the remaining marinade (reserve a small amount for serving, if desired) and bring it to a gentle simmer. In a separate bowl, whisk together cornstarch and cold water to make a slurry. Once the marinade is simmering, stir in the cornstarch mixture and cook until the sauce thickens, about 2 minutes. Set aside.
Heat a large skillet or grill pan over medium-high heat. Remove chicken from the marinade, letting the excess drip off, and cook for about 5-7 minutes per side or until fully cooked and golden brown. Use a meat thermometer to ensure the internal temperature reaches 165°F (75°C).
In the same skillet, add the broccoli and carrot, and sauté for about 3-4 minutes until they are tender-crisp. You can add a splash of water to help steam the vegetables if needed.
Slice the cooked chicken and add it to the skillet with the vegetables. Pour the thickened teriyaki sauce over the chicken and veggies, tossing to coat well.
Fluff the cooked rice with a fork and divide it among serving bowls. Top each bowl with the teriyaki chicken and vegetable mixture. Drizzle with reserved teriyaki sauce, if desired, and garnish with sliced green onions and sesame seeds.
Notes
Marinate the chicken for up to 2 hours for deeper flavor.