Export only non-default config drush config-export dumps my entire site config into files.

What I want is to only export config which is non-default.

ie. if I haven't changed my "automated cron settings" since installing my Drupal site, leave it out of my config.

Is this possible with drush? Some other tool?
Such a concept doesn't really exist in the config system. There is no overridden status like in cools/entity exports in 7.x.

Default config is only default config as long as it is a file in config/install. Once it is installed, it just is your configuration, there isn't really a connection anymore to the original default config file.

There is a hash in those files, so you could technically write something that looks for the default config file and compares the hash or even compare every single value. But keep in mind that default config can actually change, deciding whether you'd want your unchanged existing value or the new default is something that is surprisingly hard to do.

Not sure what you would want this for, the only thing that I can think of would be config for an install profile.