Sisters of Charity of the Blessed Virgin Mary

More commonly known as the BVMs,  their pre-Vatican II headgear was a literal Memento Mori. A council somewhere along the timeline wanted the Sisters to keep death before them at all times. 

History:

https://www.bvmsisters.org/about-us/history/

Motherhouse shown in Dehey:

https://www.bvmsisters.org/about-us/mount-carmel/

Vocational Link:

https://www.bvmsisters.org/get-involved/vowed-membership/