Preheat the oven to 350ºF. Butter and flour a 9-inch cake or tart pan.
In a large bowl, separate the whites from the yolks and set aside. Next, measure the sugar, then remove a couple of tablespoons and set aside to add to the whites when you beat them.
Set the remaining sugar aside. Measure out the all-purpose flour and transfer to a small bowl and set aside. Finally, measure out the extra-virgin olive oil, place in mixing bowl, and begin beating with an electric mixer—adding in the sugar a few tablespoons at a time until it is fully dissolved. Beat on high for a couple of minutes, then add the egg yolks and continue beating. Add the flour into the oil about a quarter at a time. Mix in the vanilla extract, cinnamon, and allspice; mix to combine. Set mixture aside.
Add a pinch of salt to the egg whites. Begin beating with an electric mixer until stiff peaks form—adding in the few tablespoons of sugar to the whites throughout. Using a spatula, gently fold the egg whites into the oil batter until thoroughly combined.
Lightly spread half the batter into the prepared pan. Sprinkle a bit more than half of the chopped fruit over the batter in the pan, then top with the remaining batter. Finally, spread the remaining fruit over the top and place in oven. Bake for about 45 minutes—until the top is golden brown and a toothpick comes out clean when inserted into the middle.
Serve warm or cold garnished with plain, full fat Greek yogurt (which adds an excellent tartness) and toasted sliced almonds.