Preheat the oven to 425 degrees F. In a bowl, whisk together the soy sauce, honey, vinegar, sesame oil, garlic and ginger.
Place the vegetables on the baking sheet and cover them with half of the sauce. Toss well. Roast in the oven for 12 to 15 minutes. Meanwhile, place the chicken in a bowl and cover it with the remaining sauce.
After 15 minutes, push all the vegetables to one side. Place the chicken pieces in the marinade on the baking sheet. Add the cashews on the sheet as well. Roast again for 12 to 15 minutes, until the chicken is cooked through.
Toss everything together on the sheet before serving. Serve over rice and sprinkle with green onions and sesame seeds.