In a small saucepan, whisk together soy sauce, honey, garlic, ginger, and sesame oil. Bring to a simmer over medium heat.
Stir in the cornstarch slurry and continue to cook until thickened, about 2 minutes. Remove from heat and set aside.
Heat oil in a large skillet over medium-high heat. Add chicken, season lightly with salt and pepper, and cook until browned and cooked through, about 6 to 8 minutes.
Add broccoli and carrots to the pan and sauté until crisp-tender, about 4 minutes.
Pour the teriyaki sauce over the chicken and vegetables, stirring until everything is coated well.
Serve the mixture over bowls of cooked brown rice. Garnish with sesame seeds and green onions.