In a bowl, whisk together soy sauce, honey, brown sugar, rice vinegar, sesame oil, garlic, and ginger.
Mix water and cornstarch in a small bowl, then stir into the marinade.
Place chicken in a large bowl or zip-top bag and pour half the marinade over it. Reserve the remaining marinade.
Marinate chicken in the refrigerator for 30 minutes.
Preheat grill to medium-high heat.
Thread chicken, bell peppers, onion, and zucchini onto skewers, alternating ingredients.
Grill kabobs for 10–12 minutes, turning occasionally and brushing with reserved marinade.
Cook until chicken reaches an internal temperature of 165°F (74°C).
Remove from grill and garnish with sesame seeds and green onions if desired.
Serve warm.