A bracing mint filling is sandwiched between crisp chocolate cookies and coated with a thin layer of dark chocolate in this homemade version of beloved Australian treat.
Line two baking sheets with parchment. In a medium bowl, whisk together cocoa powder, flour, and salt; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream together butter and granulated sugar on medium speed until light and fluffy, about 3 minutes. Add egg and vanilla; beat until well incorporated, scraping down sides as necessary. Reduce speed to low, add flour mixture, and mix until just combined; do not overmix. Transfer dough to a piece of plastic wrap, shape into a disk, and wrap tightly. Refrigerate at least 1 hour.
In the bowl of an electric mixer fitted with the paddle attachment, beat together confectioners' sugar, corn syrup, butter, and peppermint until well incorporated. Transfer filling to a piece of plastic wrap, shape into a disk, and wrap tightly. Refrigerate at least 1 hour.
Preheat oven to 350 degrees. Roll out dough between two sheets of parchment to a 1/8-inch thickness. Using a 3-inch oval cookie cutter, cut out ovals and place 1 inch apart on prepared baking sheets. Bake until dry, 10 to 12 minutes. Let cool on sheets 5 minutes, then transfer to wire racks to cool completely.
Roll out filling between two sheets of parchment to a scant 1/4-inch thickness. Using the same cutter, cut out ovals and sandwich between two cookies.
Place 8 ounces chocolate in a metal (or other heatproof) bowl. Set bowl of chocolate over a saucepan containing 2 inches of water (don't let bottom touch the water). Heat over medium and bring to just below a simmer. Let melt, stirring gently until chocolate registers 115 degrees on thermometer. Remove bowl; add remaining 4 ounces chocolate to bowl, stirring constantly until chocolate registers 85 degrees. Return bowl to saucepan off the heat and stir constantly until chocolate registers 89 degrees. Use immediately, stirring frequently while using to maintain temper and prevent streaking once chocolate hardens. If tempered chocolate thickens too much during use, place over simmering water again, stirring, 2 to 3 seconds.
Working with one at a time, place each sandwich in tempered chocolate and turn to coat completely. Transfer to a fresh parchment-lined baking sheet. Working quickly with the back of the tines of a fork, gently tap top of each sandwich to create a design, then slide to another location on parchment to prevent a border from forming. Let stand until set, at least 30 minutes.