Apparently cookie settings are configurable via a link on the site footer. I found this out thanks to a brief mention on the Advertising Guidelines update:
Opt in or out of cookie tracking
To opt in or out of cookie tracking, scroll down all the way to the bottom of any page on Stack Overflow or a Stack Exchange Site. Under the “Company” heading click “Cookie Settings”. There you can change your cookie preferences.
This isn't where I'd have expected these settings to be - I don't often have a reason to view/check the footer.
It would be nice if there was a way for logged in users to configure them from the User settings page - even just a link that opens the same modal that the footer shows would suffice.
I originally raised this on the aforementioned Ad Guidelines Update meta, but it was suggested to break this into it's own feature request.