In a medium bowl, combine the chicken pieces with 2 tablespoons of soy sauce and cornstarch. Toss to coat and let marinate for about 15 minutes.
In a small bowl, whisk together the remaining soy sauce, sesame oil, rice vinegar, honey, and sriracha. Set aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the garlic, ginger, and sliced bell peppers. Stir-fry for about 3 minutes until the vegetables are tender-crisp.
Add the broccoli and cook for an additional 2 minutes. Return the chicken to the skillet and pour the sauce over the mixture. Stir well to combine and cook for another 2-3 minutes until everything is heated through.
Stir in the cashews and green onions just before serving. Serve hot over cooked white rice.