Cook the brown rice: In a medium saucepan, bring 2 cups of water to a boil. Add the brown rice, reduce heat to low, cover, and simmer for 40-45 minutes until rice is tender and water is absorbed. (Note: You can start this earlier to save time.)
Prepare the teriyaki sauce: In a small bowl, whisk together soy sauce, honey, rice vinegar, sesame oil, minced garlic, and grated ginger.
Mix cornstarch and cold water in a separate small bowl until smooth and set aside.
Steam the broccoli: Place broccoli florets in a steamer basket over boiling water, cover, and steam for 5-6 minutes until tender but still crisp. Remove and set aside.
Heat olive oil in a large skillet over medium-high heat. Add chicken pieces and cook for 6-8 minutes, stirring occasionally, until fully cooked and lightly browned.
Pour the teriyaki sauce into the skillet with the chicken. Stir well 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 evenly.
To assemble the bowls, divide the cooked brown rice evenly among four bowls. Top each with steamed broccoli and teriyaki chicken.
Garnish each bowl with toasted sesame seeds and sliced green onions before serving.