Mix the sauce.
In a small bowl, whisk soy sauce, hoisin, oyster sauce, rice vinegar, sesame oil, honey, and red pepper flakes. Add water to reach a pourable consistency. Taste and adjust for sweet, salty, and heat balance.
Prep the chicken. Pat dry and dice finely.
Toss with cornstarch if using; it helps the meat brown and the sauce cling.
Cook aromatics. Heat oil in a large skillet over medium-high. Add onion and cook 2 minutes until starting to soften.
Stir in garlic and ginger for 30 seconds, until fragrant.
Brown the chicken. Add chicken to the skillet in an even layer. Let it sear undisturbed for 1 minute, then stir and cook 4–6 minutes until no longer pink.
Add vegetables.
Stir in bell pepper and mushrooms. Cook 2–3 minutes until tender-crisp.
Sauce it up. Pour in the sauce and simmer 1–2 minutes, stirring, until it slightly thickens and coats the chicken.
Add a splash of water if it gets too tight.
Finish with cashews. Stir in chopped cashews and half the green onions. Turn off the heat.
Assemble.
Spoon warm filling into lettuce leaves. Top with remaining green onions and cilantro if using. Serve immediately.