Prep the lettuce: Wash and thoroughly dry the lettuce leaves. Keeping them dry ensures they stay crisp and hold the filling without tearing.
Cook the aromatics: Heat sesame oil in a skillet or wok over medium heat. Add onion, garlic, and ginger; sauté until fragrant, about 2 minutes.
Cook the chicken: Add the ground chicken and cook, breaking it apart with a spoon, until it is no longer pink (~5–6 minutes).
Flavor the filling: Stir in soy sauce, hoisin sauce, rice vinegar, and sriracha. Simmer 2–3 minutes to allow the flavors to meld. Fold in grated carrot, water chestnuts, and green onions. Taste and adjust seasoning.
Make the peanut sauce: In a bowl, whisk together peanut butter, soy sauce, rice vinegar, lime juice, honey, and chili paste. Add warm water a spoonful at a time until smooth and pourable.
Assemble the wraps: Place spoonfuls of the spicy chicken mixture into lettuce leaves. Drizzle with peanut sauce and garnish with cilantro, lime juice, and crushed peanuts.
Serve immediately: Arrange wraps on a platter for a fun, shareable, restaurant-style experience.