SSL_shutdown() failed - No Sites will Load after 3.6.1 upgrade

I’m getting the following error after upgrading from 3.6.0 to 3.6.1:

2016/05/31 09:00:27 [crit] 19730#0: *103178 SSL_shutdown() failed (SSL: error:140E0197:SSL routines:SSL_shutdown:shutdown while in init) while SSL handshaking, client: 213.221.152.23, server: 0.0.0.0:443

I have about 13 sites all using SNI for SSL, and I’ve rebooted the server, restarted Nginx, PHP, and MySQL, but all sites will still not load. An example is https://friday-next.com.

Any idea why 3.6.1 would cause this SSL issue?