As explained in this awesome article, Phoenix is actually very modular and works as a set of libraries playing well together but that can be used independently.
The webserver part is handled by Plug which is probably what you are looking for. There is an hello world example in the doc which is fairly compact. To be more precise, Plug defines a common interface for webservers, the more popular one is
plug_cowboy which is wrapping the Erlang cowboy webserver.