Place 2 lettuce leaves in centers of wrappers, leaving 1-inch border along edges. Top each with 1/3 cup chicken mixture, 2 heaping tablespoons drained carrot mixture, 2 heaping tablespoons cucumber, slightly less than 1 tablespoon green onion and 1 large or 2 small basil leaves. Roll up wrappers over fillings, stopping after first turn to tuck in sides. Continue to roll up, tucking in sides. Place seam side down on serving plate. Repeat with remaining wrappers.