APEX configuration problem - empty stack trace

This post is just here to save someone a few hours debugging one day.

We were trying to launch a new Tomcat instance, but we were facing a strange error.

There was no stack trace, and the debug trace started with
[TE] url-mapping start:
[TE] get /ords/f?p=ABC start:

Turns out we had listed some hostnames in the workspace isolation feature, in preparation for deep linking.

Our new server was not listed.