Web GUI for Arduino (without Serial)

I'm trying out a project and I'm looking to be able to pass commands from a website to my Arduino Due.

The website will be running on a raspberry pi, connected to on the local network. I've got it working using a python CGI script passing Serial commands to Arduino, but that has an issue that it resets the arduino every time the script is run (i.e. every time a new value is recieved), that won't work for my purposes.

Would preferably like to be able to control it from either my laptop or my phone (ios).

Are there any good ways I could go about this?