In a medium bowl, whisk together soy sauce, rice vinegar, brown sugar, sesame oil, grated ginger, and minced garlic until the sugar dissolves; set the sauce aside.
Heat a large skillet over medium-high heat and add 1 tablespoon olive oil.
Add the chopped broccoli and diced red bell pepper to the skillet, season with salt and pepper, and sauté 3–4 minutes until crisp-tender; remove the vegetables and set aside.
Add the remaining 1 tablespoon olive oil to the hot skillet, add the cubed chicken seasoned with salt and pepper, and sear without stirring for 3–4 minutes to brown one side.
Stir or flip the chicken pieces and cook another 3–4 minutes until cooked through; remove the chicken and set aside.
In a small bowl, whisk the cornstarch with 1/4 cup cold water until smooth.
Return the skillet to medium heat, pour in the reserved sauce, then stir in the cornstarch mixture and cook, stirring, until the sauce comes to a boil and thickens; reduce heat and simmer 1 minute.
Return the cooked chicken to the skillet and toss to coat in the sauce, then add the cooked vegetables and stir just until everything is evenly coated and heated through.
Serve the chicken and vegetables over cooked rice and garnish with chopped green onions and sesame seeds.
