Heat the oil: In a large skillet over medium heat, add olive oil and swirl to coat the pan.
Cook the chicken: Add the ground chicken and cook for 5–7 minutes, breaking it apart with a spatula, until no longer pink and lightly browned.
Add garlic and ginger: Stir in the minced garlic and ginger and cook for another 1–2 minutes, letting the aromas develop.
Stir in the sauces: Add soy sauce, hoisin sauce, rice vinegar, sesame oil, and sriracha (if using). Mix well and simmer for 2–3 minutes so the flavors combine.
Prepare the toppings: While the chicken cooks, wash and dry the lettuce leaves. Shred the cabbage and carrots and chop the green onions.
Assemble the wraps: Spoon the warm chicken mixture into each lettuce leaf. Top with cabbage, carrots, green onions, cilantro, and sesame seeds or peanuts if using.
Serve immediately: Enjoy your wraps fresh and warm for the best crunch and flavor.