Marinate the Chicken:
In a medium bowl, combine chicken with soy sauce, cornstarch, and sesame oil. Toss to coat and let sit for 15 minutes.
Prepare the Sauce:
In a small bowl, whisk together soy sauce, hoisin sauce, rice vinegar, brown sugar, cornstarch, chicken broth, garlic, and ginger. Set aside.
Cook the Chicken:
Heat 1 tbsp vegetable oil in a large skillet or wok over medium-high heat. Add chicken and cook for 4–5 minutes until browned and cooked through. Remove chicken and set aside.
Cook the Vegetables:
Add remaining 1 tbsp oil to the skillet. Stir-fry bell peppers and snow peas for 2–3 minutes until tender-crisp.
Combine and Finish:
Return chicken to the pan. Pour in the sauce and stir to coat. Cook for 1–2 minutes until sauce thickens. Stir in cashews.
Serve:
Garnish with green onions and sesame seeds if desired. Serve hot over steamed rice or noodles.