Make the peanut sauce. In a bowl, whisk peanut butter, soy sauce, fish sauce, lime juice, rice vinegar, honey, sriracha, and sesame oil. Add warm water a little at a time until smooth and pourable.
Taste and adjust for sweetness, salt, and heat.
Prep the lettuce. Separate lettuce leaves, rinse, and pat completely dry. Keep them chilled so they stay crisp. Choose leaves that can hold a few spoonfuls of filling without tearing.
Cook the aromatics. Heat oil in a large skillet over medium-high.
Add onion and cook 2–3 minutes until softened. Stir in garlic and ginger and cook 30 seconds until fragrant.
Brown the chicken. Add ground or diced chicken to the skillet. Season lightly with salt and pepper.
Cook, breaking up the meat, until no longer pink and lightly browned, about 5–7 minutes.
Add the veggies. Stir in bell pepper, carrot, and the white parts of the green onions. Cook 2–3 minutes to soften slightly while keeping some crunch.
Sauce it up. Pour about two-thirds of the peanut sauce over the chicken mixture. Toss to coat and let it bubble for 1–2 minutes until glossy.
If it looks dry, add a splash of water or more sauce. Remove from heat and stir in a squeeze of lime.
Assemble the wraps. Place a spoonful of warm chicken into each lettuce leaf. Drizzle with extra peanut sauce.
Top with cilantro, green onion greens, chopped peanuts, and a dash of sriracha if you like it spicy.
Serve immediately. Bring lime wedges to the table for a bright finish. Enjoy while the lettuce is crisp and the filling is warm.