Preheat the oven to 350°F (180°C).
Grease the springform pan and line the bottom with a round of parchment paper.
Cream the butter until smooth, then add the sugar and vanilla sugar and mix well. Add the eggs one at a time, beating well after each addition.
Sift the flour and baking powder together, then add them to the mixture. Mix until just combined, then gradually whisk in the milk in two additions.
Stir in the shredded coconut until evenly incorporated. For an extra apple flavor, you can also fold in a few small diced apples. Pour the batter into the prepared pan and smooth the top.
Mix the sugar, cinnamon, and a pinch of nutmeg together to make the topping.
Arrange fairly thick apple slices over the entire surface of the cake, then sprinkle the topping evenly over the apples.
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 chilled, according to your preference.
For an extra touch, sprinkle with a little shredded coconut before serving.