Prepare the syrup with hot water and rum, vial and sugar, mix well so that the sugar has dissolved completely. (skip this step if the baba has already been soaked in rum before).
Arrange the baba in a tray preferably with high edges, so as not to pour the contents outside the plate, at this point, pour the syrup over the baba, taking care to soak it well according to your tastes. (If the baba is still dry, prepare some more dips and repeat the process).
Whip the sweet cream with the sugar, once whipped, add a 90g jar of pistachio cream.
Cut the baba in half and stuff with the pistachio cream obtained previously.
Finally, sprinkle with grains or pistachio flour, according to your tastes.