Total time: 35 minutes.
Combine first 5 ingredients in a large bowl; stir with a whisk. Add chicken and next 5 ingredients (through parsley) to mayonnaise mixture, tossing to coat.
Heat naan according to the package directions, if desired.
Spoon about 3/4 cup chicken mixture onto each naan. Top with 3/4 cup watercress; fold over.