How to redirect URLs without break a FastCGI app

(I consider this question a duplicate of Lighttpd redirect from
www.domain.com to domain.com, but that one didn't get enough
attention and it's too old).

I'm trying to deploy an app over lighttpd+FastCGI and encrypt all
the traffic. It works well if I explicitly use HTTPS in the URL,
but as soon I try the redirect from HTTP to HTTPS the URLs the app
script name (in this case, index.py) is included in the URL, so
instead of https://somedomain.com/bleh I get
https://somedomain.com/index.py/bleh, which triggers a Not Found error.

I tried moving some stuff around, but I can't get how to do the
redirect well. Here's the relevant stuff of my lighttpd.conf

$SERVER["socket"] == ":80" {
    $HTTP["host"] =~ "(.*)" {
        url.redirect = (
            "^/(.*)" => "https://%1/$1"
        )
    }
}

$SERVER["socket"] == ":443" {
    ssl.engine = "enable"
    ssl.pemfile = "certificate.pem"
    ssl.use-sslv2 = "disable"
    ssl.use-sslv3 = "disable"
}

fastcgi.server = (
    "index.py" => ((
        "socket" => "/tmp/app.socket",
        "bin-path" => "index.py",
        "max-procs" => 1,
        "bin-environment" => (
            "REAL_SCRIPT_NAME" => ""
        ),
        "check-local" => "disable"
    ))
)

url.rewrite-once = (
    "^/favicon.ico$" => "/static/assets/favicon.ico",
    "^/static/(.*)$" => "/static/$1",
    "^/(.*)$" => "/index.py/$1"
)