Slice the peeled apples thinly. Brush the springform cake pan with vegetable oil. Place the apple slices at the bottom as if you were making a hand fan.
Preheat the oven to 180 C (350 F).
Meanwhile, in a medium-sized bowl, beat eggs with a whisk or with a fork. Add sugar and continue to beat the eggs with a mixer for 5 minutes.
Gradually add flour, vanilla sugar, baking powder, and nutmeg and mix well. The batter will look like the one for pancakes, maybe a little bit thicker. No need to add more flour.
With a tablespoon, cover the apples in the baking form with the batter. Spread the batter between the apples. Then sprinkle the top with pieces of walnut.
Bake for 30 minutes. Put aside to cool.
In about 20 minutes, remove the cake from the form, put it on a cake platter, and dust it with powdered sugar. It is optional, in this recipe we used walnut pieces to garnish.