Rinse the brown rice under cold water until water runs clear.
In a medium saucepan, combine the brown rice and 2 cups of water. Bring to a boil over high heat, then reduce heat to low, cover, and simmer for 40-45 minutes until rice is tender and water is absorbed. Remove from heat and let stand covered.
While the rice cooks, prepare the teriyaki sauce: In a small bowl, whisk together soy sauce, honey, rice vinegar, grated ginger, and minced garlic.
In a separate small bowl, mix the cornstarch with 1/4 cup water until smooth to create a slurry.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chicken pieces and cook for 6-8 minutes, stirring occasionally, until cooked through and lightly browned. Remove chicken from skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of olive oil. Add broccoli florets, sliced carrot, and red bell pepper. Stir-fry for 4-5 minutes until vegetables are tender-crisp.
Return the cooked chicken to the skillet with the vegetables. Pour the teriyaki sauce over the mixture and bring to a simmer.
Slowly add the cornstarch slurry to the skillet while stirring continuously. Cook for 2-3 minutes until the sauce thickens and coats the chicken and vegetables evenly.
Fluff the cooked brown rice with a fork and divide it evenly among four bowls.
Spoon the chicken teriyaki mixture over the rice in each bowl.
Garnish each bowl with toasted sesame seeds and sliced green onions before serving.