In a pot, mix the water with the oil and a pinch of salt, put it on the fire and let it boil, then set it aside. Add the sifted flour and mix very well. Leave to cool.
After it has cooled a bit, add the eggs one by one, mixing very well after each one. Get a dough like a paste. Put the dough in a posh with a large tip. In a tray lined with baking paper form the donuts, and bake them on the right heat for 15-20 minutes, until lightly browned.
In a smaller pot put 400 ml of milk to boil. Meanwhile, mix the yolks with the sugar, flour and milk. When the milk starts to boil, take it off the heat, add the previous composition (flour, sugar, vanilla sugar and 100 ml of milk) and mix continuously. Put it on the fire again and let it boil until it thickens, stirring constantly so that no lumps form. Then let the pudding cool, covered with a transparent foil. We then fill the donuts, either with a posh that we stick in each donut, or by cutting a little, but without breaking them in two.
Melt the chocolate together with the cream on a steam bath, then add the 2 teaspoons of water and mix well. Pour the warm icing over the donuts, and then serve! Good appetite!!!