HTTPS with ESP8266WebServer?
The ESP8266 just doesn't have sufficient CPU power to do this reliably. 

It is possible, since the EPS8266 SDK docs have an "SSL User Manual" which describes this scenario.

In my experience, using the Arduino core for ESP8266, it doesn't work reliably.

Consider using an nginx reverse-proxy and having that proxy handle SSL negotiation. Understand that this is more for situations where the ESP8266 is local, in a network sense, to the nginx proxy, and you consider your WLAN secure enough.

On the plus side, you have room to grow in key sizes and/or complexity.