In a small bowl, whisk together soy sauce, honey, rice vinegar, 1 tablespoon water, grated ginger, and minced garlic to make the teriyaki sauce.
In a separate small bowl, mix cornstarch with 1 tablespoon water until smooth to create a slurry.
Place the chicken pieces in a medium bowl and pour half of the teriyaki sauce over them. Toss to coat and let marinate for 10 minutes.
Preheat the air fryer to 380°F (193°C) for 3 minutes.
In a large bowl, combine red bell pepper, yellow bell pepper, zucchini, and broccoli. Drizzle with olive oil and season with salt and black pepper. Toss to coat evenly.
Place the marinated chicken pieces in the air fryer basket in a single layer. Cook for 10 minutes, shaking the basket halfway through cooking.
After 10 minutes, add the mixed vegetables on top of the chicken in the air fryer basket. Cook for an additional 8-10 minutes until the chicken is cooked through and vegetables are tender-crisp, shaking the basket halfway through.
While the chicken and vegetables are cooking, pour the remaining teriyaki sauce into a small saucepan and bring to a simmer over medium heat.
Stir in the cornstarch slurry and cook, stirring constantly, until the sauce thickens, about 1-2 minutes. Remove from heat.
Once the chicken and vegetables are done, transfer them to a serving dish and drizzle the thickened teriyaki sauce over the top.
Garnish with toasted sesame seeds and sliced green onions before serving.