Arduino based web server without html - example projects?

I want to set up an Arduino based web service to accept programmatic requests (unique string to be parsed) from automated systems on a single, shared API key authenticated endpoint.
This would accept POST requests and be on either an Uno with ethernet shield or, more likely, an esp8266 based board.

So far I've found many projects which have an html form but none with only programmatic access.

Could someone please help point me in the right direction with this?

Thanks

An HTTP GET request can, despite its name, send data from a web client to a web server, and is easy to test from a web browser.
You simply build the request in a similar format to the URL which you sometimes in your browser address bar. Example: http://dataHandler.myweb.com/abc?TEMP=37&HUMIDITY=50

Search for "arduino web client http get statement"

or for a post example:

what does "programmatic access" mean?