Varnish 3.0 and Drupal 7, get registered user to always have non-cached content
You seem to be missing Vary: Cookie in addition to Vary: Accept-Encoding. You may add it in vcl_deliver using something like this:

if (resp.http.Vary !~ "Cookie") {
    set resp.http.Vary = resp.http.Vary + ", Cookie";
    set resp.http.Vary = regsub(resp.http.Vary, "^,\s*", "");
}