Stir pudding powder, 5 tablespoons of milk and 2 tablespoons of sugar until smooth. Bring the rest of the milk to the boil and remove from the stove. Stir in the pudding powder, bring to the boil and simmer for about 1 minute, stirring continuously. Pour into a bowl and let it cool down, stirring several times.
Grease a fat pan (approx. 32 x 39 cm; deep baking tray) and dust with flour. Cream 250 g butter, 250 g sugar, vanilla sugar and 1 pinch of salt with the whisks of the mixer.
Stir in the eggs one by one. Mix 350 g flour and baking powder and stir in two portions. Put the dough on the fat pan and smooth it down.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Peel, quarter and core apples. Cut the apple quarters into 1-2 mm deep several times lengthwise on the curved side. Stir crème fraîche into the pudding.
Spread the pudding mixture on the dough by the spoonful, pressing it flat a little with the back of the spoon. Place the apple quarters on top with the curvature facing upwards. Bake in the oven for about 30 minutes.
Knead 100 g butter and brown sugar and spread as flakes on the cake, bake at the same temperature for another 25-30 minutes. Let it cool down. Serve with whipped cream.