Pressing Ctrl+Shift+Del
brings up the deletion dialog in almost all browsers (I\'ve tested IE, Firefox, and Chrome), where you can delete cookies,
I assume your Authentication cookie is a session cookie. That will be deleted when the browser closes, and is typically stored in memory only. Since it's already that private, it makes little sense (from a privacy viewpoint) to delete it even quicker.
Now, some browsers may still delete it early. When they happen to have a unified cookie store, it's easier to just delete all cookies. But for browsers that handle session cookies separately, there's no good reason to duplicate the cookie deletion logic.