2011 iMac running Sierra
I would like to have a copy of macOS that I can actually boot from and use on a USB key, so that I can run Carbon Copy Cloner from it to make backups of any volume on the machine at any time. I previously had a dedicated small partition on one of my drives for this purpose, but that drive died and going forward I would rather have this on a USB stick.
To be clear, I don't want a "bootable installer". I want a fully functional bootable macOS on the stick, i.e. it boots into Finder, etc. All the answers I've found related to this, are about creating bootable installers.
Can this be done and if so, how?