For the cake: In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl if you’re using a hand mixer, beat the eggs with the maple sugar and melted butter until the mixture is pale and fluffy, about 3 minutes. In a small separate bowl, whisk the almond flour, all-purpose flour, baking powder, and salt together. Add half of the mixture to the wet ingredients, stirring just to combine. Add the milk, stir to incorporate, then stir in the remaining dry ingredients. Do not overmix. Set the cake batter aside while you prepare the caramel.
Make the caramel: In a large nonstick skillet or saute pan set over medium heat, melt the butter, then whisk in the maple sugar, Cognac (if using), vanilla seeds, and salt. Bring to a full boil and let it roll 1 minute. Lower the heat to medium heat, then add the apple slices and cook for 3 minutes. Take the skillet off the heat and use a fork or a spoon to carefully pick up the apple slices and transfer them to the bottom of the prepared springform pan. Try to set them side by side to create a pretty pattern (remember the slices will show off on top of the dessert!) Pour an extra 1/4 cup (60 ml) of caramel over the apples. Strain the remaining caramel into a glass jar.
Pour the batter over the caramelized apples. Bake for 20 minutes or until a toothpick inserted in the center of the cake comes out with a few crumbs attached to it. Let the cake cool completely in the pan, set over a wire rack.
SERVING: Loosen the springform pan and unmold the cake. Place an inverted serving plate over the cake, then turn it over. Carefully lift the bottom of the springform pan off the top of the cake, running a sharp knife under it to detach apple slices that stick, if necessary. Spread more warm caramel over the top of the cake right before serving. This cake is absolutely dreamy served with a scoop of vanilla bean gelato!
STORAGE: This cake is best enjoyed within 2 days. You can make the cake in advance and let it cool to room temperature in the pan. Cover the pan with plastic wrap and refrigerate. Refrigerate the extra caramel as well. Before serving, reheat the cake in a warm (175°F / 80°C) oven for 15 to 20 minutes, then invert onto a serving plate. Reheat the caramel in the microwave for a few seconds before serving.
NOTE: Don’t throw that seeded vanilla pod away! Add it to a jar of sugar to make vanilla-infused sugar, add them to simmering jams, or use them to infuse warm milk or cream that will be used to make hot chocolate, gelato, ice cream, custards, panna cotta, or sweet sauces.
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