Cream the butter at room temperature until it reaches a mayonnaise-like consistency.

Add powdered sugar to the butter and mix well.

Mix in egg yolks and rum, adding one yolk at a time.

Sift and add cake flour to the mixture. Fold gently using a cutting motion.

Divide the dough into two portions. Add cocoa powder to one portion and mix until combined.

Roll out both dough portions to equal thickness and chill in the freezer for 30 minutes.

Brush egg white on the larger dough sheet and place the smaller sheet on top. Roll tightly into a log.

Chill the rolled dough overnight in the freezer.

Slice the dough into 0.7-1cm thick pieces and insert ice bar sticks into the center.

Preheat the oven to 180°C for 20 minutes. Bake the cookies for 15-16 minutes.