To make dipping sauce, combine the soy sauce, vinegar and sugar in a small saucepan. Stir over a low heat until the sugar has dissolved. Set aside to cool.
Bring the stock and ginger to the boil in a large frying pan over a medium heat. Add the chicken. Reduce to a simmer, then cover the pan and cook for about 12 minutes or until the chicken is opaque, turning it over halfway through the cooking. Remove the chicken from the pan (discard the stock). When cool enough to handle, shred the chicken.
Pour the vinegar and soy sauce into a medium bowl and stir together. Add the shredded chicken, carrot and red capsicum and toss to combine.
Place the lettuce leaves, hollow-side up, on the work surface. Place a mint leaf in each lettuce leaf. Dividing it evenly, spoon the chicken mixture into the lettuce leaves and sprinkle the peanuts on top. Roll up the leaves and serve with the dipping sauce in a bowl.