Post #7:
https://www.backyardchickens.com/t/663464/what-causes-soft-shell-eggs
Also look here:
http://www.blpbooks.co.uk/articles/egg_problems/egg_problems.php
Has she always laid eggs like this or is it a recent thing?
If you don't want to put her down you can make her stop laying for awhile and it seems the easiest and healthiest way of doing that is to make her days shorter, i.e. reduce her light hours to about 10 hours a day. Hopefully that will help!