Preheat the oven to 400 degrees F (200 degrees C). Line an 11-inch round baking pan with parchment paper.
Combine sliced apples, 1/2 cup white sugar, butter, and brown sugar in a large bowl. Mix together gently, being careful not to break apple slices. Pour sugary juice from the apple mixture into the prepared baking pan. Arrange sliced apples on top in a circle. Sprinkle raisins on top of apples and pour any remaining juice over all.
Combine olive oil and cinnamon in a large mixing bowl. Add egg yolks, flour, grated apples, baking powder, and remaining white sugar. Stir well to combine. Beat egg whites to a light froth in a separate bowl and stir into the olive oil mixture carefully. Pour over the apples in the baking pan.
Bake in the preheated oven until a knife inserted in the center comes out clean, about 45 minutes. Cover cake with foil if the top browns before the cake is done baking.
Remove cake from oven and allow to cool, about 30 minutes. Invert cake onto a serving plate.