In a small bowl, whisk together soy sauce, brown sugar, rice vinegar, sesame oil, garlic, and ginger. Set aside.
In another small bowl, mix cornstarch and water until smooth. Set aside.
Heat vegetable oil in a large skillet over medium-high heat. Add chicken pieces and cook until browned and cooked through, about 5-7 minutes.
Pour the teriyaki sauce over the cooked chicken in the skillet. Stir to coat the chicken evenly.
Add broccoli and carrots to the skillet, stirring to combine. Cook for an additional 3-4 minutes until vegetables are tender-crisp.
Stir in the cornstarch mixture and cook for another 1-2 minutes until the sauce thickens.
Serve the teriyaki chicken and vegetables over cooked rice. Garnish with sliced green onions and sesame seeds.