The instructions[0] say it's included in Ubuntu 17.04 and later, but I couldn't see any way of enabling it.
I tried installing with apt using the command they listed:
. /etc/os-release
sudo apt install -t ${VERSION_CODENAME}-backports cockpit
But this didn't work. Eventually I read on another website that this is the correct way to install it: sudo apt install cockpit -y
This probably would be obvious for most people - but since this software is all about improving server UX, I thought it was worth mentioning!