Preheat the oven to 350 F. Grease a 9-inch springform pan, and line the bottom and sides with baking parchment.

Peel, halve, and core the apples. Place each apple half cut-side down on a cutting board and use a sharp knife to cut parallel thin slices halfway through--in other words, you want to "score" the apple half but not actually create slices that will separate. It can be helpful to place a chopstick or similar item against one side of the apple, to help stop you from slicing too far down. (If you do cut all the way through, however, no worries, you can just place the smaller pieces together on top of the batter.)

Transfer the scored apple halves to a medium bowl and toss with the lemon juice and 2 tablespoons sugar.

In another medium bowl, whisk together the all-purpose flour and almond flour. Set aside.

In a large bowl, use electric beaters to cream together the butter and 75 g sugar until light and fluffy. Add the maple syrup and beat until incorporated. Now add the egg yolks, vanilla, and almond extract, beating until just combined. Sprinkle over the baking powder and salt, and beat until they just disappear. Now add the flour mixture, half at a time, mixing in until just combined.

In a separate bowl with clean beaters, whisk the egg whites until stiff peaks form.

Add 1/4 of the whisked egg whites to the batter, to lighten it, then add the remainder, using a rubber or silicone spatula to fold them in until just *barely* combined. (A couple faint streaks of egg white are okay.)

Scrape the batter into the prepared pan and smooth the top. Arrange the apple halves over the batter--no need to press them down; they'll sink naturally as the cake bakes. If there is any sugary lemon juice left in the apple bowl, you can drizzle it over the apples. Sprinkle flaked almonds around the apples.

Bake the cake 45 to 50 minutes, until a tester inserted in the center comes out clean.

Remove the cake from the oven, and allow it to cool in the pan on a wire rack. After 10-15 minutes, if you wish, you can release the sides of the springform pan. Either way, however, wait until the cake is completely cool before transfering it to a serving plate. Dust the cooled cake with powdered sugar.