Peel the apples, remove the cores, and cut them into thin slices. Place the fruit in an appropriately sized ovenproof dish.

Mix sugar and cinnamon and sprinkle it over the fruit. Toss to distribute the sugar and cinnamon evenly.

Pour flour into a bowl.

Cut cold butter into small pieces and add it to the flour.

“Chop” the flour and butter together and then crumble it with your fingers until it resembles grated cheese.

Add sugar and mix everything until it resembles a crumbly dough. Do not knead the dough; it should remain crumbly.

Spread the crumble over the apples in the dish.

Bake the cake for approximately 35 minutes at 200 degrees Celsius (392 degrees Fahrenheit) until the crumble is golden and crisp.

If the surface is too pale near the end of the baking time, turn on the oven's fan function and give the cake a final blast with the fan.

Dissolve cornstarch in 100 ml of the milk in a bowl until the mixture is completely smooth and lump-free.

Add eggs, sugar, and vanilla sugar, and whisk the mixture well with a hand whisk.

Pour a small amount of water into the bottom of a heavy-bottomed pot and bring it to a boil.

When the water boils, add the rest of the milk.

Bring the milk to a boil while stirring constantly.

When the milk boils, remove it from the heat and pour it into the bowl with the cornstarch mixture. Whisk the mixture at high speed, then pour everything back into the pot.

Bring the cream sauce to a boil while stirring constantly. Let it boil for a couple of minutes to remove the taste of cornstarch.

Pour the cream sauce into a bowl and sprinkle the surface with a little sugar (this prevents the formation of a skin on the surface).

Let the cream sauce cool until it is warm.

Serve the apple cake with the cream sauce.