This is as far I guess that you can get off the beaten path. Well, at least it is a very good attempt to do so! These are two tiny, tiny villages on the edge of the Penada-Gerês National Park in Northern Portugal (which is actually the only designated National Park in Portugal).
I got a tip about these villages from tourist office inside the National Park, after mentioning that I would like to visit some really off the beaten paths spots. And he was spot on with his tip, as I thoroughly enjoyed my visit. It is so off-the beaten path that it might be tuff to find it on your map ;-)
The first visit was to the village of Branda d'Aveleira. This is the one closest to the National Park and seems the one best known.
Branda de Santo António
The second visit was to the village of Branda de Santo António.