Make the cookie dough

1. Whisk together the melted butter, egg white and peppermint extract in a large bowl.
2. Sift the flour, cocoa and icing sugar over the wet mix and stir with a spatula until the mixture begins to come together. Toward the end, use your hands to form a cohesive dough.
3. Divide the dough into three portions. Work with one portion at a time and keep the others covered.

Roll and cut

1. Place one piece of dough between two large sheets of baking paper. Roll very thin (aim for roughly 1 mm). Carefully peel back the top sheet of paper, then replace and flip the dough so you can remove the other sheet — this helps loosen it from the paper.
2. Use a square cutter about 10 cm (4 in) across (round cutters work too) to stamp out shapes. Move away excess dough as you go.

Form the rolls

1. Position a half-straw about 5 mm from the front edge of a cut piece. Lift the front edge with an offset spatula or small knife and wrap the dough around the straw, rolling gently until you have a neat tube. Transfer tubes to a lined baking tray, spacing them about 2–3 cm (1–1½ in) apart. Repeat with remaining dough and straws.
2. Chill the trays in the refrigerator for at least 30 minutes — this step helps the rolls keep their shape in the oven.

Bake & unmold

1. Preheat the oven to 200°C (400°F) or 180°C fan (fan-forced). Bake the chilled rolls for about 10 minutes, until dry to the touch.
2. Remove from oven and cool 5–10 minutes. To extract a straw, hold the cookie gently in one hand and push the straw through from one side until it slides out the other. Allow cookies to cool fully before filling.

Prepare the peppermint fondant

1. In a mixer, beat the softened butter with glucose (or corn syrup) and a pinch of salt. Add half the icing sugar and beat until light. Add the remaining icing sugar, then stir in the peppermint extract and about half the milk. Add more milk a teaspoon at a time until the mixture pipes easily but still holds shape.

Fill the rolls & finish

1. Fit a small piping tip to a bag and pipe the peppermint cream into the center of each tube from one end, then from the other, until the filling reaches the middle. Don’t overfill.
2. Line a tray with baking paper and place a wire rack on top. Melt the dark chocolate in short bursts in the microwave, stirring between intervals to avoid burning. Dip each tube end into the melted chocolate and immediately sprinkle with crushed candy cane. Set on the wire rack until the chocolate firms.

Quick alternate method (no rolling)

1. If you prefer not to roll tubes, cut rounds from slightly thicker rolled dough and bake 8–9 minutes. Sandwich two rounds together with the peppermint cream and dip the edges in chocolate and crushed candy cane.