Sure you can, you just need an anonymous voting mechanism that's sufficiently naive. You use the verifiable process to restrict access to that anonymous mechanism.
In Canada, at both federal and provincial levels, you walk up to a desk and identify yourself, are crossed off a list, and handed a paper ballot. You go behind a screen, mark an X on the ballot, fold it up, take it back out to another desk, and put it in the box. It's extraordinarily simple.
> At some point, you have to give someone access to a database and they can change that database.
Well, that kind of fraud is a different issue from someone reading the database and figuring out who someone voted for (you just... don't record identities in the database).
> you walk up to a desk
I think the day I _must_ walk go a desk to vote is the day I'll give up. Voting by mail is one of the best things occuring here (in Switzerland). You get the voting stuff by mail, make your crosses, put it back into the postal box and it's delivered for free (as in beer) to the government.
> paper ballots and requiring IDs
isn't that racist? i've heard it repeated but i'm not so sure
There will never be a technical or operational process that excludes cheating. The only deterrence that seems to work on humans and even then only most of the time is severe capitol punishment and that will only be as effective as people believe it happens thus requiring live streaming of the removal of cheaters heads without censorship. The current legal process of each country would have to be by-passed or people would just sit in a cage for 30 years. Even in such cases there will be people that sacrifice themselves if they think that bribe money can go to their family but that is at least a start.