Preheat your oven to 375°F (gas mark 5, 177°C) and line two baking sheets with parchment paper or a silicone baking mat.
In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl (you can use a hand mixer just fine), stir together the flour, sugar, baking soda, baking powder and salt.
Cut the softened butter into tablespoons and using the low speed on your mixer, stir in the butter, egg and vanilla extract. Mix until well combined. The dough will be on the drier side, but should still stick together.
Use a tablespoon or small cookie scoop to portion out your cookie dough on your baking sheets. Slightly flatten each disc. You'll have enough for 18-20 sandwich cookies.**
Bake the sheets for 10 minutes, rotating once halfway through baking time. Allow the cookies to set for 5 minutes on the sheet before transferring to wire racks to cool completely. Make the filling while the cookies are cooling.
Filling
Cream together the butter and cream cheese until light and fluffy.
Stir in the sugar 1 cup at a time, and then add the peppermint extract.
Assemble the cookies by placing your filling into a piping bag or plastic bag, snipping off the tip, and piping about a tablespoon on one cookie, top with a second cookie. Enjoy!