In a large bowl, whisk together the egg yolks, sugar, rum, and lemon zest.
In another bowl, mix the flour with the butter using clean hands or a pastry cutter, until the mixture has a crumbly texture.
Gradually incorporate the egg mixture into the flour-butter mixture, stirring until a dough begins to form. Shape the dough into a large log, wrap it in plastic wrap, and refrigerate for 20 minutes.
Preheat your oven to 325°F (160°C) and prepare two baking sheets by lining them with parchment paper.
Slice the dough into 12 portions. Roll each portion into a strip-like log and shape into “S” or “O” forms. Place the shaped cookies onto the baking sheets.
Brush the tops with the beaten egg white.
Bake for 13–18 minutes, or until the edges turn golden. Let the cookies cool slightly and enjoy!