Pat the chicken breasts dry with paper towels. If the breasts are particularly thick (over 1 inch), pound them slightly to achieve even thickness.
In a small saucepan, combine soy sauce, mirin, honey, brown sugar, garlic, ginger, and rice vinegar. Bring to a gentle simmer over medium heat.
In a small bowl, mix cornstarch and cold water until smooth to create a slurry.
Add the cornstarch slurry to the simmering sauce, whisking constantly. Continue to simmer for 2-3 minutes until the sauce thickens to a glaze-like consistency. Remove from heat and stir in sesame oil.
Reserve half of the teriyaki sauce for basting later. Pour the remaining half over the chicken breasts in a shallow dish or zip-top bag. Marinate for 10-30 minutes.
Preheat your air fryer to 380°F (193°C) for 3-5 minutes.
Remove the chicken from the marinade, letting excess drip off. Place chicken in the air fryer basket, ensuring pieces don't touch for optimal air circulation. Cook for 6 minutes.
Open the air fryer and brush the chicken with a thin layer of the reserved teriyaki sauce. Return to cooking for 3-4 more minutes.
Check the internal temperature with a meat thermometer. The chicken should register at least 155°F (68°C) at this point.
Apply a second layer of teriyaki glaze and continue cooking for 2-4 more minutes, until the chicken reaches 165°F (74°C) and the glaze appears caramelized but not burnt.
Remove the chicken from the air fryer and let it rest for 3-5 minutes to allow juices to redistribute.
Slice against the grain, drizzle with remaining teriyaki sauce, and garnish with sliced green onions and sesame seeds.