Line two baking sheets with parchment paper or a silicon mat.
Sift the flour, corn starch, and cocoa together. Mix in the salt.
Cream the butter and sugar together in a food mixer for 2 minutes until fluffy.
Add in the flour and mix until combined.
Add just enough milk to form a stiff dough ball.
Roll the dough to 1/8" and cut or stamp into rectangles 60mm x 30mm or 2" x 1". Stamp if you like, or if not just prick holes across the biscuit with a skewer or fork.
Add sprinkling sugar, if using.
Preheat oven to 350F.
Chill biscuits for 30m in fridge, then bake for 12-15m. Once baked, cool on a wire rack.
To make filling:
Cream the butter in a food mixer until fluffy, and then gradually mix in the confectioner's sugar.
If making the chocolate version, heat chocolate in a bowl over a hot water bath until just melted, then cool to room temperature. Add to the butter and sugar and mix until combined.
If making the peanut butter variation, add the peanut butter into the butter and sugar.
If making the matcha version, dissolve the matcha powder in the milk, then add to the other ingredients.
Sandwich two biscuits together with a little of the filling, and store refrigerated until ready to serve. Biscuits should keep for 3-4 days.