Preheat the oven to 350 F and line a baking tray with parchment paper; set aside.
Add the flour, butter, sugar, sugar, cocoa powder, and baking soda to a large bowl or in a bowl of stand mixer. Mix the ingredients on medium speed until just combined.
Add the milk in batches, a little at a time, and mix until a dough is formed.
Roll out the dough on a lightly floured surface to 1/4-inch thickness. Cut out cookies using a 2-inch round cookie cutter.
Place the cutouts on the prepared baking tray and bake for 12-15 min in a preheated oven. Let the cookies cool for 5 minutes in the baking tray before transferring them to a wire rack to cool completely.
Mint Cream Filling
In a bowl of a stand mixer or using a hand mixer, cream the butter until it's light and fluffy.
Add peppermint extract, vanilla extract, a few drops of green gel food color and sugar (in batches). Beat until you get a smooth and fluffy consistency (5-6 min).
Fill a piping bag with the prepared frosting and attach a round-tip nozzle. Pipe the frosting onto the flat side of one cookie and then place another cookie on top, flat side down. Press gently to make a sandwich.