In a medium bowl, whisk together the peanut butter, soy sauce, honey, rice vinegar, sesame oil, minced garlic, and grated ginger until smooth and well combined.
In a large mixing bowl, combine the shredded chicken with half of the peanut sauce, mixing until the chicken is well coated.
Lay out the lettuce leaves on a clean surface. Spoon an equal amount of the chicken mixture onto each lettuce leaf.
Top the chicken with shredded carrots, sliced bell peppers, and chopped cilantro.
Drizzle additional peanut sauce over the top if desired.
Sprinkle with chopped peanuts for added crunch, if using.
Carefully fold the sides of the lettuce leaves over the filling and roll them up tightly. Serve immediately.