Preheat the oven to 180°C (350°F)
Grease and line the bottom of the springform pan with a round of parchment paper.
Cream the butter, then add the sugar and vanilla sugar, mixing well. Add the eggs one at a time, beating after each addition.
Sift the flour and baking powder together, then add them to the mixture. Mix until combined, then gradually whisk in the milk in two additions.
Stir in the shredded coconut until evenly incorporated, then pour the batter into the pan and smooth the top.
Arrange fairly thick apple slices over the entire surface of the cake.
Sprinkle with the mixture of sugar, cinnamon, and a pinch of nutmeg.
Bake for 50 minutes to 1 hour, depending on your oven. A skewer inserted into the center should come out clean.
Let the cake cool slightly, then remove it from the pan and transfer it to a wire rack. Serve warm, at room temperature, or cold, according to your taste.