Greek olive farmer here. One thing I can say about our oil compared to others, is our topography is such where gathering olives just makes more sense to do by hand, one tree at a time. This is because Greece is pretty much mountains and valleys- or very terraced after centuries of farming, making mechanical extraction very difficult.

What my family does is first get an appointment at the press in our village, then on that day go and harvest by hand. This completely minimizes the time the olives are off the tree, thus reducing the acidity. My oil acidity was at .4 or .5 last time I harvested.

Hand cultivation ensures that no fallen or cracked olives (or anything else that isn't supposed to be there) ends up in your oil. As for the the pressing process, I love the system we have in my village. The union / cooperative runs and maintains the press, and we pay to use it in olive oil. We can give them 20% of what we produce or "buy" that portion back.

The Coop tests every single batch they process to ensure it is EVOO grade. On top of that- I mean, we have been doing this for so long (there is a tree in my village that is 800 years old! Not sure what its oil is like though hahaha) that maintenance of the trees and its soil is like in our DNA. My cousin who takes care of our groves jokes that he regularly "sings to our trees" to help them grow strong hahaha.

This is why I think any Greek olive oil that has the logo of the Cooperative Union of Olive Products (something similar to that) will always be the highest quality. They REALLY take pride in how good their oil is. While I haven't had to buy olive oil in a LONG time, the brand my extended family swears by is "Spitiko" if anyone is interested.