Hi BigFactHunt,
Thanks for reaching out in Apple Support Communities. I understand that you're seeing "nsurlsessiond" using over 60% CPU after upgrading to macOS Catalina. I can see why you'd reach out about this; I'd like to help. This process is typically related to iCloud data such as iCloud Photos or iCloud Drive updating on your Mac.
Are you using iCloud Photos on your Mac? You can check this from System Preferences > Apple ID > iCloud. If Photos is enabled, the process you're seeing could be related to that and may take some time for the sync to iCloud to complete.
If you do not want to wait for the process to complete, are you able to stop the process in Activity Monitor? Does it resume on its own?
Let me know what you find.
Best Regards.