I am writing an HTTP proxy and I am having trouble understanding some details of making a CONNECT request over TLS. To get a better picture, I am experimenting with Apache
It is quite seldom to see CONNECT Method inside TLS (https). I actually don't know any client who does that (and I would be interested to know who it does, cause I think it is actually a good feature).
Normally the client connects with http (plain tcp) to the proxy and sends the CONNECT method (and host header) to host:443. Then the proxy will make a transparent connection to the endpoint and then the client sends the SSL handshake through.
In this scenario the data is ssl protected "end to end".
The CONNECT method is not really specified, it is only reserved in the HTTP RFC. But typically it is quite simple so it is interoperable. The Method specifies host[:port]. Host: header can simply be ignored. Some additional proxy authentication headers might be needed. When the body of the connection begins no parsing has to happen by the proxy anymore (some do, because they check for valid SSL handshake).