In a large mixing bowl, whisk together ½ cup of melted and cooled unsalted butter, 1 large egg white, and 1 teaspoon of peppermint extract until smooth and frothy.

Sift together 1 ½ cups of plain flour, ½ cup of Dutch process cocoa, and 1 cup of icing sugar directly into the wet ingredients. Mix until a soft dough begins to form.

Divide the dough into three equal pieces and roll each piece into a rectangle about ¼ inch thick.

Place a paper straw at one edge of the rectangle and gently roll the dough around the straw to form a tight cylinder.

Carefully place the rolled cookies on a baking tray and refrigerate for at least 30 minutes.

Preheat your oven to 350°F (175°C) while the rolls chill. Bake for approximately 10 minutes.

In a bowl, combine ¼ cup of softened unsalted butter, 1 cup of icing sugar, 2 tablespoons of liquid glucose, a pinch of salt, and sufficient milk to achieve a smooth consistency.

Fill each cooled roll with the creamy peppermint filling. Melt 1 cup of dark chocolate and dip each filled cookie end into the chocolate.

Before the chocolate sets, sprinkle crushed candy canes over the coated ends of the cookies.

Once the chocolate fully sets, serve and share your Peppermint Chocolate Roll Cookies!