My initial impressions are that TLS handshake is very computationally expensive.
Stress testing my webserver with plain HTTP connections:
7980.2744 queries/s
With HTTPS (TLS) connections:
23.059916 queries/s
The slowdown is due to high CPU usage.
I certainly wouldn't classify that as fast!
I've only done a bit of work on this so it's possible I'm misusing the LibTLS API however.