1840 was a long time ago...is there any restaurant, regardless of ownership, that is older? I suppose there may be older restaurants that have passed from one family to another over the centuries?
Correction -- from https://en.wikipedia.org/wiki/List_of_oldest_companies -- there's a construction company from the late 500s, but the oldest hotel is from 705. (But, considering that Charlemagne was born in 742, that's not too shabby.)
Drovers Inn, Inverarnan (1705) http://www.droversinn.co.uk/
The Sheep Heid, Edinburgh (allegedly 1360, but a bit vague) https://www.thesheepheidedinburgh.co.uk/
A quick search on Google showed this link:http://theculturetrip.com/asia/japan/articles/the-10-oldest-... The first listing was "Established in 1659".
It's difficult to define exactly the boundaries between tavern, tea house, and restaurant, but I'd be curious what the oldest business serving prepared meals but not offering accommodation.