For our own version of this classic French dessert, we wanted the best of both worlds: a dessert with a custardy, apple-rich base beneath a light, cakelike topping. To ensure that the apple slices softened fully, we microwaved them briefly to break the enzyme responsible for firming up pectin. And to create two differently textured layers from one batter, we divided the batter and added egg yolks to one part to make the custardy base and flour to the rest to form the cake layer above it.

• 1 1/2 pounds Granny Smith apples, peeled, cored, cut into 8 wedges, and sliced 1/8 inch thick crosswise
• 1 tablespoon Calvados
• 1 teaspoon lemon juice
• 1 cup (5 ounces) plus 2 tablespoons all-purpose flour
• 1 cup (7 ounces) plus 1 tablespoon granulated sugar
• 2 teaspoons baking powder
• 1/2 teaspoon salt
• 1 large egg plus 2 large yolks
• 1 cup vegetable oil
• 1 cup whole milk
• 1 teaspoon vanilla extract
• Confectioners' sugar

1. Adjust oven rack to lower-middle position and heat oven to 325 degrees. Spray 9-inch springform pan with vegetable oil spray. Place prepared pan on rimmed baking sheet lined with aluminum foil. Place apple slices into microwave-safe pie plate, cover, and microwave until apples are pliable and slightly translucent, about 3 minutes. Toss apple slices with Calvados and lemon juice and let cool for 15 minutes.
2. Whisk 1 cup flour, 1 cup granulated sugar, baking powder, and salt together in bowl. Whisk egg, oil, milk, and vanilla together in second bowl until smooth. Add dry ingredients to wet ingredients and whisk until just combined. Transfer 1 cup batter to separate bowl and set aside.
3. Add egg yolks to remaining batter and whisk to combine. Using spatula, gently fold in cooled apples. Transfer batter to prepared pan; using offset spatula, spread batter evenly to pan edges, gently pressing on apples to create even, compact layer, and smooth surface.
4. Whisk remaining 2 tablespoons flour into reserved batter. Pour over batter in pan and spread batter evenly to pan edges and smooth surface. Sprinkle remaining 1 tablespoon granulated sugar evenly over cake.
5. Bake until center of cake is set, toothpick inserted in center comes out clean, and top is golden brown, about 1¼ hours. Transfer pan to wire rack; let cool for 5 minutes. Run paring knife around sides of pan and let cool completely, 2 to 3 hours. Dust lightly with confectioners’ sugar, cut into wedges, and serve.

The microwaved apples should be pliable but not completely soft when cooked. To test for doneness, take one apple slice and try to bend it. If it snaps in half, it’s too firm; microwave it for an additional 30 seconds and test again. If Calvados is unavailable, 1 tablespoon of apple brandy or white rum can be substituted.