Preheat oven to 180C / 350F /160C fan forced. Line 2 large baking trays with baking paper.
Sift together the flour, cornflour, cocoa and baking soda and whisk to thoroughly combine.
In a separate bowl, beat together the butter and sugar until lightened and fluffy.
Scrape down the sides of the bowl and add half the flour mix. Beat until just combined. Add the milk and food colouring (if using), and remainder of the flour. Mix until it starts to clump.
Pull the dough together with your hands. Dust a sheet of baking paper lightly with cocoa, then the top of the dough. Roll the dough out to about 3-4mm thick and use a circle cookie cutter to cut out small circles (3-4cm or not quite 2 inches round). Re-roll as necessary.
Sit on baking trays an inch apart. Bake for around 10 minutes, turning the trays halfway through.
Allow the cookies to cool on the trays for a few minutes before using a spatula to help to transfer them to a wire cooling rack. Once cool, they will firm up and be crispy all the way through (notes).
FOR THE QUICK PEPPERMINT BUTTERCREAM
Add the butter, icing sugar, milk, peppermint extract and colouring (if using) to a bowl and beat with a handheld mixer (or in a stand mixer) until pale and creamy. Scrape down the sides of the bowl as necessary.
Spread or pipe some buttercream onto the flat side of half of the cooled cookies, then top with another cookie.
Melt the chocolate in 30 second intervals in the microwave stirring well between each until JUST melted (this should take no longer than 2 minutes). Dip the tops of each cookie into the chocolate, turn them back upright and let them set before serving.