For the dough, mix the flour with the sugar, lime zest and a pinch of salt in a bowl. Make a well in the middle of the flour mixture, add the egg and lime juice into the well, and spread the butter in small pieces around. Quickly knead with your hands to a smooth dough, shape the dough into a ball and wrap in a plastic wrap. Let the dough rest for 30 minutes in the refrigerator.
Put the dough on a floured work surface and roll out to 4 mm thin. Cut out star-shaped cookies from the rolled dough. Knead the residual dough, roll out again and cut out more star cookies.
Place the cookies on a baking tray lined with baking paper and bake in a preheated oven at 180°C (fan: 160°C, gas mark 2-3) (approximately 350°F) for about 10 minutes.
Remove the tray from the oven, allow the cookies to cool down, and remove the cookies along with the baking paper from the tray.
For the glaze, mix the powdered sugar with the cachaca rum to a thick glaze. Brush the cookies with the glaze. Decorate the cookies as desired with sugar pearls and let dry.