Preheat the oven to 350 F degrees. Lightly grease the base and sides of a 9-inch round springform pan with olive oil and line the bottom with unbleached parchment paper. Set aside.
Place the raisins and 2/3 cup of the water in a medium saucepan. Simmer over low heat until the raisins are plump, about 10 minutes. Remove from heat and drain any remaining water in the pan. Set aside.
Whisk the flours, cinnamon, nutmeg, cloves, baking soda, baking powder and salt together in a medium bowl. Peel and core the apples, then cut into 1-inch pieces and set aside in a separate bowl. The apples may start to oxidize if you do this in advance, but it’s ok because you won’t be able to tell when the cake bakes.
Place the sugar, olive oil, whole eggs, vanilla and orange zest in the bowl of an electric mixer fitted with the paddle attachment. Beat on medium speed for 4-5 minutes, until the mixture is light in color and has thickened a little. Remove the bowl from the machine and, using a large spatula, add the dry mix and gently fold to combine. Add the apples, raisins, and the remaining 1/3 cup water (or equivalent amount of calvados, if using) and stir to combine.
Place the egg whites in a clean bowl and whisk at high speed until soft peaks form. Gently fold in the egg whites into the batter, then transfer the batter into the prepared pan. Smooth the top with a spatula and bake for 40 - 50 minutes, or until a skewer inserted into the middle of the cake comes out clean. Remove from the oven, allow to cool in the pan for a few minutes. Run a thin knife along the perimeter of the cake, unmold and transfer the cake to a cooling rack to cool completely.
Once cool, you can dust with a little powdered sugar, if desired.