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:, server:

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

Any idea why 3.6.1 would cause this SSL issue?