Rinse the brown rice under cold water until the water runs clear.
In a medium saucepan, combine the rinsed rice and 3 cups of water. Bring to a boil over high heat.
Once boiling, reduce heat to low, cover, and simmer for 40 minutes or until rice is tender and water is absorbed. Remove from heat and let stand covered for 5 minutes.
While the rice cooks, steam the broccoli florets in a steamer basket over boiling water for 5-6 minutes until tender but still crisp. Remove and set aside.
In a small bowl, whisk together soy sauce, honey, rice vinegar, grated ginger, and minced garlic to make the teriyaki sauce.
Heat olive oil in a large skillet over medium-high heat.
Add the chicken pieces to the skillet and cook for 6-8 minutes, stirring occasionally, until fully cooked and lightly browned.
Pour the teriyaki sauce over the cooked chicken and bring to a simmer.
In a small bowl, mix cornstarch and cold water until smooth. Add this mixture to the skillet and stir well.
Cook for 2-3 minutes until the sauce thickens and coats the chicken evenly.
To assemble the bowls, divide the cooked brown rice evenly among four bowls.
Top each bowl with steamed broccoli and the teriyaki chicken.
Sprinkle toasted sesame seeds over each bowl before serving.