Beat the eggs with the sugar, add the flour, vanilla and 1/2 the milk. Put the rest of the milk with the butter in a pot, heat it on the stove and leave to reach boiling point.
Once the milk comes to a boil, pour the egg mixture in a thin trickle, while stirring with a whisk energetically, nonstop.
Stir the mixture until you get a thick milky cream without floury lumps. Remove from the stove, scoop from the cream with a ladle and pour it at the bottom of the tray in which you'll be arranging the cake.
Distribute the cream along the bottom, arrange a layer of biscuits, pour cream again, cover them, arrange a new layer of biscuits. Arrange cream and biscuits until out, finishing off with cream.
Cool the cake, grate chocolate on top and put it in the fridge for 6 hours to take in the cream and for the biscuits to soften.