In a large mixing bowl with a hand mixer add in the butter, and brown sugar and mix until fluffy. Add in the egg, and vanilla extract and mix, and then add the dry ingredients to the wet ingredients.
Scoop cookie dough with a cookie scoop and place it on a prepared baking sheet lined with parchment paper. Press down on the dough to flatten the dough.
Bake cookies at 350 degrees for 8 to 10 minutes. Allow the cookies to fully cool on the cookie sheet before removing them to a cooling rack.
Peppermint filling.
With your stand mixer add the butter and whip on medium speed until the butter is fluffy. Scape the sides of the bowl and then add the powdered sugar and beat for another 2 minutes on high. Add peppermint extract and then mix until combined. Fill a piping bag with a round piping tip or use a small cookie scoop to fill the cookies.
Peppermint Cookie Assembly:
With a clean work surface find and match cookies placing them next to each other. Pipe on the flat side and then sandwich the cookies together with a little bit of pressure. Prepare all cookie sandwiches and then place a wire rack.
Crush the peppermint in a food processor in a Ziplock bag and place them on a large plate. Roll the sides of the cookies into the peppermint so the side of the buttercream is covered in crushed candy canes.
Store in an airtight container for up to 5 days. Enjoy!