Put the ginger, coriander, scallions, carrot, and chicken breasts in a medium saucepan. Cover with the broth, and bring just to a boil. Lower the heat to very low and cover. Poach the chicken for 20 minutes or until firm to the touch. Remove the pan from the heat, uncover, and cool the chicken in the liquid, about 30 minutes. Bone and pull the chicken into bite-size pieces. Save the broth.
Toss the chicken with the remaining salad ingredients and toss with the dressing. Wrap about 1/3 cup of the salad in a lettuce leaf. Serve 3 to 4 lettuce leaves per person with a wedge of lime if desired.
Whisk the lime juice, ginger, soy, chili, fish sauce, salt and broth in a small bowl. Gradually whisk in the oil, starting with a few drops and then adding the rest in a steady stream, to make a dressing.
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