In a small bowl, whisk together soy sauce, brown sugar, rice vinegar, sesame oil, minced garlic, and grated ginger. Set aside.
Cut the chicken thighs into bite-sized pieces. In a large skillet, heat vegetable oil over medium-high heat. Add the chicken and cook until browned and cooked through, about 5-7 minutes.
Pour the sauce mixture over the chicken in the skillet. Stir to coat the chicken evenly.
In a separate small bowl, mix cornstarch and water until smooth. Add this mixture to the skillet and stir well. Cook for an additional 2-3 minutes until the sauce thickens.
While the sauce is thickening, steam the broccoli and carrots until tender, about 3-4 minutes.
To assemble the bowls, divide the cooked rice among four bowls. Top with the teriyaki chicken and vegetables.
Garnish with sliced green onions and sesame seeds before serving.