Beat the eggs with the sugar, milk and vanillas. Caramelize the sugar with the water. Pour the caramel into a rectangular form.
Arrange pieces of the bananas on top. Then arrange a layer of biscotti. Place slices of bananas again, biscotti, bananas and finish with biscotti.
Pour the beaten eggs and milk over them. Leave them for a few minutes to absorb the milk (I pressed down on them slightly because they float up when soaking it in). Bake in a water bath at 320°F (160 °C) for about 60 min.
Leave them to cool and invert carefully onto a platter. Optionally, you can make a caramel and pour it over the cake. Put it in the fridge for several hours before serving.