Fixing Broken Link Checker 'Unknown error' on HTTPS URLs

Recently I’ve encountered a strange issue with the Broken Link Checker plugin for Wordpress:

While all HTTP URLs work just fine, every single HTTPS URL yields an Unknown error without any log message or explanation.

Additionally, the server error log on my VPS does not contain any errors related to link checking.

After some digging around I found out that the plugin internally uses curl to check HTTPS links.

I just needed to

sudo apt-get install php-curl

on my Ubuntu 16.04 system in order to get HTTPS URL checking to work and subsequently tell the plugin to re-check every failed URL.