For the dressing, combine all the ingredients except for cilantro in a blender and process until smooth. Add cilantro and blend a few seconds until the cilantro is finely chopped. Refrigerate until ready to serve.
For the lettuce wraps, lay out lettuce leaves on plates. Two leaves per wrap. Place shredded chicken on butter lettuce leaves, then top with shredded carrots and chopped cilantro. Drizzle peanut dressing then sprinkle black sesame seeds.
