Beat the 8 eggs, sugar and vanilla. To the resulting mixture, add the flour, which you've mixed with the baking powder and half the carbonated water.
Divide up the mixture into 3 identical bowls. Add the cocoa to one of them for the brown layer, leave the others yellow. Bake the cake layers 1 by 1 in a buttered and floured tray.
To make the cream, put 3 4/5 cups (900 ml) of the milk in a pot to boil on the stove with the sugar and vanilla for it.
Next, beat the yolks with the flour and remaining milk, pour this in a thin trickle into the pot, while stirring nonstop. Add the butter. Leave the cream to cool a bit.
Stack the cake layers, alternating between yellow, brown and yellow, while pouring carbonated water on top of each layer to syrup them, pour cream and then place the subsequent layer.