Marinate the chicken: Add the chicken to a large bowl. Stir together the soy sauce, dry sherry, and arrowroot powder in a small bowl, then pour on top of the chicken. Toss together and set aside while prepping your sauce.
Make the kung pao sauce: In a small bowl, whisk together the water, soy sauce, dry sherry, rice vinegar, honey, sesame oil, and arrowroot powder. Set aside.
Dry roast the nuts: Heat a large saute pan or wok over medium-high heat and dry roast the nuts for a minute, stirring them constantly until lightly toasted. Remove them to a bowl.
Cook the chicken: Heat 2 tablespoons of oil in the pan over medium-high heat. Add the chicken and stir fry for 3 to 4 minutes, until cooked through and lightly golden. Remove from the pan and set aside.
Add the peppers and aromatics: Add another tablespoon of oil to the pan (if needed) along with the bell pepper, dried chili peppers, garlic, ginger, and Sichuan powder, and stir fry for 3 to 4 minutes.
Combine everything together. Re-stir the sauce (to make sure the flour hasn't settled on the bottom of the bowl), and pour it into the wok. Add the green onion and chicken, and stir fry for a minute or two, until the sauce starts to thicken and turn glossy. Turn off the heat, add the cashews and give it a final stir to combine.
Serve: Serve the kung pao chicken plain or over rice.