OMG, y'all, this is so GOOD!
1/2 cup unbleached all-purpose flour, plus more for the pan
2 teaspoons baking powder
pinch of sea salt
2 large eggs, at room temperature
1 cup sugar, preferably organic
1 teaspoon vanilla extract
1/2 cup milk
7 tablespoons unsalted butter, melted and cooled slightly, plus more at room temperature for the pan
4 large firm-fleshed apples (1 3/4 pounds), peeled, cored, quartered, and cut crosswise into 1/8-inch slices
Powdered sugar, for garnish
Preheat the oven to 375 degrees.
In a small bowl, combine the flour, baking powder, and salt. Set aside.
Place the eggs, sugar, and vanilla extract in the bowl of an electric mixer. Whisk on medium speed until the sugar has dissolved and the mixture is pale and thick, about 30-60 seconds.
Fold the flour into the egg mixture with a wooden spoon until just incorporated. Fold in the milk, then the butter and finally the apple slices. Be sure not to overmix.
Butter and flour a 10-inch nonstick springform pan. Pour the mixture into the prepared pan. Pack the apples into the mold and flatten the surface of the cake with the wooden spoon.
Bake for 10 minutes on the floor of the oven. Transfer the pan to the middle rack and continue baking until golden brown and a toothpick inserted into the center comes out clean, for 50-55 minutes.
Remove the cake from the oven, and run a paring knife around the edge to loosen the cake from the ring of the mold. Let cool in its mold to room temperature. Unmold the cake and transfer to a serving platter. Dust with powdered sugar and serve.
Note: The cake can be baked up to 6 hours ahead and kept in its mold at room temperature in a cool place. It is best eaten the day it is made.