I have tried a few things:
127.0.0.1
the duck duck go start page
brave(dot)com
and a few others. Some real websites, some not. None work.
Brave only starts with the updates.bravesoftware update URL:
I do have Brave locked and set to read only. Does not seem to keep it safe as it updated again about an hour ago - which I trashed and reinstalled my last working copy which still works but is a bad work around.