Doughnuts with custard

NGREDIENTS
720 g flour
4 eggs
18 cl of milk
70 g sugar
6 cl water
60 g butter
22 g baker's yeast
1 pinch of salt

Cream :
50 cl milk
4 egg yolks
110 g sugar
60 g cornstarch
20 g butter
1 vanilla pod

Icing :
80 g icing sugar
2 tbsp water

PREPARATION
Put the sifted flour in a large bowl, add the sugar and salt and mix. Make a well, add the yeast diluted in 1/2 glass of slightly warm milk. Mix together the eggs, milk and water. Add to the well and mix. Add the softened butter little by little and mix well. Cover with cling film and set aside for at least 1 hour, then chill for 2 hours.
The cream:
Heat the milk with the vanilla pod cut in half. Mix the yolks with the sugar and cornflour. Pour this mixture into the milk from which you have removed the vanilla pod. Mix well. Once the cream has thickened, remove from the heat and add the butter, turn well and leave to cool. Then put in the fridge.
On your floured work surface, roll out your pastry with a rolling pin and cut out circles with a glass or cookie cutter 6 cm in diameter and 1 cm high. Place your pasta circles on a baking tray covered with baking paper and leave to rise for another 30-45 minutes. Heat your frying oil and cook the fritters. Set aside on absorbent paper.
Mix the icing sugar and water. Then dip half of the doughnuts in it and let them harden.
Once they have cooled, fill them with the cream. To do this, cut them in half.