Zeytinyağlı is a style of preparation in Turkish cuisine in which vegetables or legumes are cooked in olive oil. Zeytinyağlı taze fasulye are flat green beans (they are called fagioli a corallo in Italian, I have no idea what the English equivalent is) cooked in with lots of onion and tomatoes. The ideal result is a bean that is firm, not soft as it is so often prepared, with a sweet condiment.
Your Grandma Cipollina used to make this. I called it string beans with tomatoes and onions – origninal?
Well, food from the Balkans and E Europe has a lot in common with Turkish food, so im not surprised. I think I can remember that dish. I definitely remember the melted butter she used to make. There were green beans in that.