We should add callbacks for libcurl's CURLOPT_DEBUGFUNCTION to log to our logging system. The set parameter should set CURLOPT_VERBOSE in createCurlEasyHandle in src/mongo/util/net/http_client_curl.cpp
 
We should log CURLINFO_TEXT, CURLINFO_HEADER_IN, and CURLINFO_HEADER_OUT. But we should check what libcurl does by default to stdout and align towards.