Pion[0] is a fairly robust and well-written HTTP server implementation in C++. You can spin up a server very quickly and reverse proxy through Apache or Nginx. Microsoft has a cross-platform offering of some sort in the works using C++11, now I don’t remember the name but I think Herb Sutter has a write-up in it from a couple years ago. It’s definitely possible to write modern web applications in C++, I feel like the cgi route is pretty old school.
[0] https://github.com/splunk/pion