Make the sauce. In a small bowl, whisk soy sauce, hoisin, rice vinegar, brown sugar, water, sesame oil, cornstarch, and optional chili.
Set aside. The cornstarch will help the sauce thicken quickly.
Prep the chicken. Pat chicken dry. Toss with 1 tablespoon oil, cornstarch, and black pepper until evenly coated.
This light coating gives the chicken a silky, tender texture and helps it brown.
Heat the pan. Set a large skillet or wok over medium-high heat. Add 1 tablespoon oil and swirl to coat. You want it hot before the chicken hits the pan.
Sear the chicken. Add chicken in a single layer.
Cook 4–6 minutes, stirring only once or twice, until browned and cooked through. Transfer to a plate.
Sauté aromatics. In the same pan, add onion and bell pepper. Cook 2–3 minutes until crisp-tender.
Add garlic, ginger, and the white parts of the green onions. Stir 30 seconds until fragrant.
Combine and simmer. Return chicken to the pan. Whisk the sauce again (cornstarch settles), then pour it in.
Stir and let it bubble for 1–2 minutes until glossy and slightly thickened.
Add cashews. Stir in cashews and the green onion tops. Cook 30 seconds more to warm the nuts and coat everything in sauce.
Taste and adjust. Add a splash more water if the sauce is too thick, or a pinch of sugar or vinegar to balance the flavors. Serve hot over rice.