Preheat the oven to 450 degrees F (230 degrees C). Grease a shallow 2 quart baking dish.
Place the pitted prunes in a saucepan with enough water to cover. Bring to a simmer, and cook until the prunes are tender but still hold their shape, about 10 minutes. Drain the prunes and arrange them in the bottom of the prepared baking dish.
Whisk together the flour, white sugar, vanilla sugar, baking powder, and salt in a large bowl. Whisk in the eggs one at a time, beating well after each addition. Gradually pour in the milk, stirring vigorously with a wooden spoon until combined. Stir in the rum. Pour the batter evenly over the prunes.
Bake in the preheated oven for 10 minutes. Reduce the oven temperature to 400 degrees F, and bake until the filling is firm, has risen a little, and the top is browned, about 30 minutes. Serve warm or at room temperature.
