Season the chicken pieces with salt and pepper, then coat them in cornstarch, toss well to coat. Dip the coated chicken into beaten eggs.
Preheat the air fryer to 380 degrees F (193°C) for 3-5 minutes. Place the chicken pieces in the air fryer basket in a single layer, spraying them lightly with cooking spray or olive oil. Set cook time for for 10-12 minutes, flipping halfway through, until the chicken is golden and cooked through. The internal temperature should be 165 degrees F.
In a large saucepan, add the soy sauce, hoisin sauce, rice vinegar, sesame oil, brown sugar, garlic, ginger, and red pepper flakes. Over low-medium heat, bring the mixture to a simmer. In a small bowl, prepare the cornstarch slurry, by adding cornstarch and water, and mix well, until the mixture is smooth. Slowly, add the cornstarch slurry and stir continuously until the sauce thickens.
In a large saucepan or skillet, sauté the bell pepper and onion until tender.
Add the air-fried chicken and cashews to the skillet with the vegetables. Pour the sauce over the chicken and vegetables, tossing everything to coat evenly.
Serve your spicy cashew chicken with rice or noodles.