How to get self-referencing https request to work in Local?

I’ve discovered that Local sites cannot call their own API’s because they do not have an entry for their own public hostname in /etc/hosts on the server. (I have a feature request about this, if anyone cares to vote to fix it.)

The server’s /etc/hosts file should including the line: mysite.local

I’ve added this manually and while it works for http requests, I still have trouble with https requests which fail with:
curl: Failed to connect to rea.local port 443: Connection refused

I’d love a suggestion about how to make port 443 requests from the server to the server work.