ASP.NET WebForms Authentication Logout, Cookie can still be used to access site

I have been banging my head against the wall and searching the web for this but I think I am having issues understanding the whole process of logging users out of an asp.net webforms application. The issue:
I am able to log in to my application and it uses cookies, so I have my cookie set in the browser.
here is the config forms authentication section,

Hide an ASP.NET Menu Item

I have an ASP.NET webforms application with a Menu control. How does one hide a particular menu item via code? I’ve seen a few articles pointing out how to do it with ASP.Net membership/roles-based security, but this particular use case has nothing to do with that. I simply need a way to programmatically remove a menu item from code. Any help would be appreciated.