In a casserole, combine water, brown sugar and rum and bring to boil. Turn off the heat, add prunes and let them soak for at least 3 hours.
When ready, bring them back to boil, reduce the heat and cook until you obtain confiture (jam) consistency, for about 30 minutes. If you find the process too long, just get rid of some juice.
Place the prunes into a food processor and pulse to obtain a thick sauce. Set aside.
In a deep mixing bowl, beat egg yolk with icing sugar, then add butter, vanilla extract, salt, baking powder and flour. Work the dough with your hands to form a ball. Place in the fridge for 1 hour.
Using your hands, spread the dough over the bottom and slightly over the edges of a round 20 cm baking dish. Gently press down with your palms and fingers to even out the surface.
Peel and slice the bananas, place them over the bottom of the dough, then pour over the prune sauce.
Bake at 180°C for 25 minutes.
Let cool down, then place in the fridge for a couple of hours and dust with icing sugar before serving.