Preheat oven to 400°F (≈200°C) and spray or line a large sheet pan.
In a saucepan over medium heat, combine soy sauce, honey, rice wine vinegar, sesame oil, garlic, ginger, cornstarch, water, and salt & pepper. Bring to boil, then simmer ~5 minutes until glaze thickens.
While glaze simmers, place chicken pieces in center of sheet pan. Toss broccoli, carrots (and optional veggies) with a little oil; spread them around chicken.
Drizzle ~⅔ of the teriyaki glaze over chicken and vegetables, using a brush or spoon to coat.
Bake for 20–25 minutes, until chicken reaches 165°F and vegetables are tender and caramelized at edges.
Remove from oven; drizzle remaining glaze over finished dish.
Serve over rice, garnish with chopped green onions and sesame seeds.