Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper or foil for easy cleanup.
In a mixing bowl, whisk together soy sauce, honey, sesame oil, garlic, ginger, and cornstarch until well combined. Set aside.
In a large bowl, add the chicken pieces and season with salt and pepper. Pour half of the sauce mixture over the chicken and toss until fully coated.
On the prepared sheet pan, spread the marinated chicken pieces out evenly.
In the same bowl, add the broccoli, red, and yellow bell peppers. Drizzle with olive oil and the remaining sauce mixture, and toss to evenly coat.
Spread the vegetables around the chicken on the sheet pan without overcrowding.
Roast everything in the preheated oven for 20-25 minutes, stirring halfway through, until the chicken is cooked through (internal temperature of 165°F) and the vegetables are tender yet crisp.
Remove from the oven and sprinkle toasted cashews on top. Return to the oven for an additional 3-5 minutes to warm the cashews.
Garnish with sesame seeds and sliced green onions before serving.