Soak the prunes in the rum for 24 hours, stirring them periodically.
Beat the eggs, sugar and vanillas to a fluffy cream and add the sifted flour and starch, while stirring nonstop.
Then pour the milk in a thin trickle, again while stirring, until the mixture homogenizes.
Pour the liquid mixture into an oiled cake form with high walls. Pour the prunes on top and put the pudding cake to bake in a preheated to about 338°F (170 °C) oven on the lower element for about 80-90 min.
Serve the Pudding Cake cut into slices.