In a mixing bowl, whisk together the soy sauce, honey, rice vinegar, mirin, minced garlic, and minced ginger until well combined to prepare the teriyaki marinade.
Place the chicken breasts in a sealable plastic bag or shallow dish and pour half of the marinade over the chicken. Seal the bag or cover the dish and marinate in the refrigerator for at least 15 minutes or up to 4 hours.
After marinating, remove the chicken from the marinade, allowing excess liquid to drip off. Discard the used marinade.
In a skillet or frying pan, heat the vegetable oil over medium heat. Once hot, add the chicken breasts and cook for about 6-7 minutes on each side, or until fully cooked.
Combine the remaining marinade, cornstarch, and water in a small saucepan. Cook over medium heat, stirring continuously until the sauce thickens, about 3-5 minutes.
Once the chicken is cooked, remove it from the skillet and let it rest for a few minutes before slicing.
Drizzle the thickened teriyaki sauce over the sliced chicken in a serving dish and garnish with sliced green onions and sesame seeds before serving.