Pour the sugar in a tray, distribute it evenly and add the diced butter. Cook on low heat to a golden caramel.
Cut the peeled apples into thin crescents and arrange them next to each other on top of the caramel in a fan.
In a bowl, beat the eggs with the rest of the sugar, add the flour that you've mixed with the baking powder and stir to a smooth mixture.
Pour the mixture over the arranged apples and bake in a preheated 356°F (180 °C) oven until the cake is ready.
While still hot, invert the cake into a suitable plate. There's caramel left over in the tray, so pour in 1 cup water and put it in the hot oven to melt.
Pour the resulting syrup over the cake, leave it to cool completely before serving.