For the apple tart, cream the softened butter with the powdered sugar. Add the eggs one by one, beating lightly.
Sift in the flour and knead into the dough. Do not beat any more. Let the dough cal rest for 1 hour in a cool place.
In the meantime, for the topping, peel and quarter the apples, remove the core. Melt the sugar in a saucepan with the water and bring to a boil.
Briefly bubble the apple quarters in sugar water. Drain and set aside. Preheat the oven to 200 degrees. Butter a 26 cm diameter cake springform pan.
Roll out the dough thinly on a floured work surface and line the tart springform pan with it. Raise the edge. Place the pan on the middle rack in the oven and pre-bake the dough for 10-15 minutes.
In the meantime, for the cream, boil the milk with sugar. Whisk the egg yolks with the milk in a wide saucepan until creamy, add the boiling milk and heat everything together, stirring throughout, but do not let it bubble up.
Cover the pre-baked pastry base with the drained apple quarters. Spread the cream evenly on top. Put the pan back into the oven, increase the temperature to 220 degrees and bake the cake for about 25 minutes.