Place egg whites into a mixing bowl with sugar, and beat with an electric mixer until the mixture forms soft peaks. Beat in egg yolks and vanilla.

Whisk together the flour with baking powder in a separate bowl, and mix the flour mixture into the beaten egg mixture until just combined.

Place butter and apples into the bottom of a 9x13-inch baking pan, and place into oven. Preheat oven to 350 degrees F (175 degrees C) to melt the butter. When oven is hot and butter has melted, stir the apples and butter together, and spread out in the pan. Pour the cake batter on top of the butter and apples.

Bake in preheated oven until the top is golden brown, about 20 minutes. Loosen the edges of the cake with a spatula, and flip the cake over onto a serving platter to serve. Allow to cool for a few minutes before eating, or serve cool.