SoupSession now has APIs for reading the response body as a GInputStream, but doesn't have APIs for writing the request body as a GOutputStream.

current theory is something like:

  GIOStream *soup_session_send_with_body (SoupSession   *session,
                                          SoupMessage   *msg,
                                          GCancellable  *cancellable,
                                          GError       **error);

First you call g_io_stream_get_output_stream() to get the request stream, write to that, close it, then call g_io_stream_get_input_stream() to get the response stream. Likewise with the async API.