Combine dressing ingredients in a small bowl. Refrigerate until needed.
Cook the vermicelli according to package directions. Rinse it with cool water and place it in a bowl when it's ready. Ribbon the carrot (I used my potato peeler to do this) or cut it into matchsticks. Slice the avocado and cucumber, and prepare the herbs and lettuce.
Fill a large bowl full of cool water. Wet a piece of rice paper and then place it on the surface you'll be assembling the rolls on.
Add the vermicelli, vegetables, and chicken to the top third of the rice paper. Fold the sides over slightly and then fold the top over so it just touches the filling. Tuck in the filling with your hands as you roll it towards you. Keep in mind you want the rolls to be fairly firm, but if you roll them too tightly, you'll break the paper.
Repeat the process for as many rolls as you have stuffing for. Serve the salad rolls with the miso dipping sauce. You can keep the rolls intact or cut them in half.