Mix flour, baking powder, vanilla and salt in a mixing bowl.
Add cold butter and chop finely.
Add sugar and rum and mix briefly.
Add egg and knead briefly and quickly to form a roughly homogeneous shortcrust dough.
Take 1/3 of the dough, divide it into 4 - 5 small pieces and place them in the freezer.
Place the remaining 2/3 of the dough in an airtight container in the fridge for 1 hour.
Take the dough out of the fridge and roll it out on a floured work surface to a thickness of approx. 3 mm.
Using a round cookie cutter or a drinking glass, cut out round cookies (in my case Ø 6 cm each) from the dough and place them a little apart on a baking tray lined with baking paper.
Coat the cookies approx. 1 - 2 mm thick with caramelized sweetened condensed milk.
First take a piece of dough out of the freezer, grate it quickly with a coarse grater and sprinkle generously over the cookies. Repeat the process with the remaining pieces of dough from the freezer and the remaining cookies.
Bake the cookies in a preheated oven at 356 °F (180 °C) for approx. 20 minutes and leave to cool on the baking tray (be careful, the filling is very hot!).
Dust the crumb cookies lightly with powdered sugar before serving.