Prep the lettuce. Rinse and gently separate the lettuce leaves.
Pat dry with a clean towel. Keep them chilled so they stay crisp.
Make the sauce. In a small bowl, whisk soy sauce, hoisin, rice vinegar, sesame oil, and sriracha. Taste and adjust heat or salt as needed.
Set aside.
Cook the aromatics. Heat oil in a large skillet over medium. Add onion and cook 3–4 minutes until translucent. Stir in garlic and ginger for 30 seconds until fragrant.
Brown the chicken. Add ground chicken, breaking it up with a spatula.
Season with a pinch of salt and pepper. Cook 5–7 minutes until no longer pink and lightly browned in spots.
Add the veggies. Stir in bell pepper and mushrooms. Cook 3–4 minutes until softened.
Fold in water chestnuts and half the green onions.
Simmer with the sauce. Pour the sauce over the mixture. Stir to coat. If you prefer a thicker glaze, add the cornstarch slurry and simmer 1–2 minutes until glossy.
Finish and taste. Turn off the heat.
Squeeze in a little lime if you like brightness. Adjust seasoning with soy sauce, pepper, or chili sauce.
Assemble the wraps. Spoon warm filling into chilled lettuce cups. Top with remaining green onions, sesame seeds, and a drizzle of sriracha if desired.
Serve immediately.