With the rack in the middle position, preheat the oven to 180 °C (350 °F). Butter a 2 litre (8 cup) capacity soufflé dish.
Cut the flesh of 1 apple into cubes. Set aside for the cake batter. Slice 1 apple into thin slices with the mandolin. Keep only the slices with the beautiful central star. Place them in a rosette pattern, overlapping them to fully cover the bottom of the dish.
With a mandolin, thinly slice the remaining apples on each side to the core. Lay the apple slices at the bottom of the dish, pressing to prevent the cake batter from seeping between the slices. Add the maple syrup. Set aside.
In a bowl, combine the flour, baking powder, cinnamon and salt. Set aside. In another bowl, cream the butter with the brown sugar with an electric mixer. Add the eggs, one at a time, beating until the mixture is smooth.
At low speed, add the dry ingredients alternately with the apple juice. Using a spatula, gently stir in the reserved diced apple. Spoon the batter into the prepared pan.
Bake for about 1 hour 30 minutes or until a toothpick inserted in the center of the cake comes out clean. Let cool for about 15 minutes. Run a thin knife between the cake and the sides of the dish. Unmould on a serving platter. Serve warm or at room temperature and drizzle with maple yogurt (see note).
If the peeled apples have to wait, keep them in lemon water to prevent darkening.
In a bowl, blend 500 ml (2 cups) 2% plain yogurt and 125 ml (1/2 cup) maple syrup.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.