In a bowl toss together the chicken, cucumber, carrot, lettuce, and sprouts.
In a small bowl, whisk together the soy sauce, sesame oil, lime juice, and honey. Pour the soy sauce mixture over the chicken mixture and toss to coat.
Soak a clean dishtowel with water and ring it out very well. Turn an 8- or 10–inch cake pan upside down and cover it with the towel.
Fill a pie plate with warm water. Dip one of the rice paper sheets into the warm water, moving it around for about 30 seconds, until it becomes translucent. (Do not leave it soaking in the water or it will become too soggy.) Quickly place the rice paper on the towel–covered cake pan and use it immediately.
Place one–quarter of the chicken mixture along the front edge of the rice paper, top with a few basil and mint leaves, and roll the rice paper into a tight summer roll shape, tucking the ends in as you roll. Repeat with the remaining rice paper sheets and chicken mixture.
Serve at room temperature, with the chili sauce on the side for dipping.
Recipe Notes
These summer rolls keep in an airtight container in the refrigerator for up to 2 days.