Whisk egg and sugar together, using a hand mixer, into a white and fluffy mixture.
Melt the butter, let it cool off a bit, and slowly mix it with the egg mixture.
In a separate bowl, mix the flour, vanilla sugar and baking powder. If you are using vanilla essence add this in the next step.
Gently mix the flour and egg mixture together using a wooden spoon.
Peel the apples and dice them. Pour the apples into the cake batter and mix.
Grease a circular baking tray with butter or lined it with baking paper. Pour the cake batter into the tray.
For topping, peel the apples and slice them. Spread them in a dense pattern on top of the cake.
Mix the cinnamon and sugar together and sprinkle it on top of the apples in an even layer.
Bake the cake at 180 C (360 F) for about 35-40 minutes. Check if the cake is done by sticking a thin wooden stick into the cake - if it's done no cake batter will stick to the stick.
Notes
Serve the apple cake warm with some sour cream or some homemade vanilla ice cream.