Preheat oven to 160°C 325°F. Position rack in the center. Line baking sheet with parchment paper.
In a large bowl whisk together the sugar, olive oil,vanilla extract and eggs. Add the flour, baking powder and salt and stir with wooden spoon until just incorporated. Fold in the plum, pistachio and almonds.
The dough is a bit sticky so wet your palms then divide into two. Place each half on a large cookie sheet, and shape into a log.
Bake for 25-30 minutes or until your logs are golden brown and firm. Let cool slightly.
Put the baked logs on a cutting board, using your sharpest knife, slice cookies about ½ - ¾ inch thick. Lay the pieces cut side down on the baking tray and put it back in the oven for 10-12 minutes, until the outside of the cookies feel toasted but they still give a little when pressed in. They will crisp up more when cooled.Let them cook for 10-15 minutes before you eat. Good luck with waiting.