Preheat the oven to 350 F / 180 C. Grease the base and sides of a 9-inch/23-cm round springform pan and line with parchment paper. The paper should rise 1-inch/3 cm above the sides of the pan (Note: I don’t own this size springform, so I just used a regular 9-inch cake pan, sprayed it with cooking spray, lined the sides with parchment and made sure the parchment extended an inch above the rim of the pan, and sprayed it again for good measure. This worked great.)Set aside.Place the raisins and 2/3 cup (160ml) of the water in a medium saucepan. Simmer over low heat until all the water has been absorbed, then set aside.Sift all of the flours, cinnamon, baking soda, baking powder and salt together into a bowl and set aside. Peel and core the apples, then cut into 1-inch/3cm dice and set aside in a separate bowl.Place the sugar, olive oil, whole eggs, vanilla and lemon zest in the bowl of an electric mixer with the paddle attachment in place. Beat on medium speed for 6-7 minutes, until the mixture is light in color, doubled in size and has thickened a little. Don’t be tempted to increase the speed of the machine when mixing; this will create air bubbles, which you don’t want. Remove the bowl from the machine and, using a large spatula, add the sifted dry ingredients and gently fold to combine. Add the apples, raisins, and the remaining 1/3 cup (80ml) water and stir to combine.Place the egg whites in a separate clean bowl and whisk to form soft peaks; there’s only a small amount of egg white here so you might need to do this by hand (I used electric hand beaters). Gently but thoroughly fold the egg whites into the cake mix, then scrape the batter into the pan. Level the top with a spatula and bake for 55 -60 minutes (slightly longer if using Granny Smiths as they take longer to soften), or until a skewer inserted into the middle of the cake comes out clean. Remove from the oven and set aside to cool in the pan.To make the maple frosting: While the cake is cooling, place the butter, brown sugar, and maple syrup in the bowl of a stand mixer fitted with the paddle attachment. Beat until light and airy, then add the cream cheese, a quarter at a time. Continue to beat for about 2 minutes, until thick and smooth.When the cake is completely cool, remove it from the pan. Spoon the frosting on top and spread evenly.Storage notes: Covered in plastic wrap, the (unfrosted) cake lasts for one week. Bring it to room temperature and frost it on the day you’ll serve it. Alternatively, we found the cake was just fine for 4 days, frosted, when covered in the fridge and the flavor actually improves the second day.