Open the “Adobe Illustrator Prefs” file with a plain text editor.
You need to right click the file and choose a plain text editor application for this file.
If you just double click, the system will use Illustrator to open it and you will only see a simple and pretty useless dialog.
(If you don’t know how to access to this file, please read my previous post: Access to Illustrator Preferences Files on Mac OS)
In the “Adobe Illustrator Prefs” file, search for:
The only thing you need to do is change the number to the right of this command AND save.
Logically if you change it to “0”, the application should stop storing any recent files.
Now restart Illustrator, you can see the number of recent files change.