1 stick unsalted butter, melted and cooled, divided into 1 tablespoon and 7 tablespoons
½ cup plus 1 tablespoon unbleached all-purpose flour, divided
5 Golden Delicious apples
2 large eggs
1 ¼ cups sugar
½ cup whole milk
1 teaspoon vanilla extract
2 teaspoons baking powder
Powdered sugar, for dusting
Use 1/2 tablespoon of melted butter to brush the inside of a 9-inch cake pan Line the bottom of the pan with a piece of parchment paper and brush the paper with the remaining ½ tablespoon of butter. Add 1 tablespoon flour and shake pan to coat completely.
Peel, core, and quarter the apples. Slice the sections crosswise into very thin slices; set aside.
Beat the eggs and sugar in a large bowl with a whisk until the sugar is dissolved and the eggs are pale yellow. Stir in the remaining flour and then add the milk, 7 tablespoons butter and vanilla. Blend the mixture, but do not overwork. Stir in the baking powder and fold in the apples.
Pour the mixture into the prepared pan and bake for 35–40 minutes. Check after 20 minutes and loosely cover with oiled foil if it is browning too quickly. The cake is done when a small paring knife inserted in the center comes out clean.
Cool the cake on a wire rack for 20 minutes. Place the rack over the pan upside down and invert. Remove the cake pan and peel off the parchment paper. Allow cooling for 15 minutes longer and then place a plate on the cake and quickly flip the cake right side up. Dust with powdered sugar and serve.