Server info in SSL handshake?

[E.B.]

Hi, today I was watching traffic on port 443 for other reasons
and I saw a line go by that had unusual information, looking
a little bit like server info headers (I saw "nginx" and the version
number and a couple other info I think maybe "REMOTE_ADDR"
or something like it). Its port 443 so it surprised me -- does
some server info leak out during the SSL handshake?

I saw it at least twice but now it isn't coming back and I wasn't
able to capture it.  :(