Caddy server has this feature baked in: https://caddyserver.com/docs/markdown

I wrote a web server that converts markdown to HTML dynamically. Not sure if it's what you're looking for but it works decently well. I host my personal site on it.

https://github.com/crempp/mdweb

I wrote one in Go called Lanyon, available at: https://github.com/mkaz/lanyon

It works pretty well, but fairly bare bones and haven't updated it in a bit.

Here's one http://harpjs.com/

Jekyll and Hugo do this statically.

I don't know about dynamic webservers.