How do you guys go about doing this? Is there some techy/reverse engineering way or you manually asking each department which domains they have?
Some TLDs gives you open access to just query the DNS and do an AXFR (download the whole zone), for example the .se and .nu ccTLDs (which I happen to work for the foundation managing those): dig @zonedata.iis.se se AXFR > se.zone.txt
For some zones you could use NSEC traversal https://linux.die.net/man/1/walker
For the new gTLDs (.app, .dev, .xyz, etc, etc) there is the Centralized Zone Data Service provided by icann: https://czds.icann.org/home where you can request access to zones.
How would I know if they have open access?
I suspect the non ssl ones aren’t holding anything particularly useful at this stage though.