01 - Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
02 - In a medium bowl, whisk together the all-purpose flour, cocoa powder, baking soda, and salt until evenly distributed.
03 - In a large mixing bowl, beat the softened butter and granulated sugar together using an electric mixer until light and fluffy, about 2 to 3 minutes. Add the egg and vanilla extract, beating until fully incorporated.
04 - Gradually add the dry ingredient mixture to the creamed butter mixture, mixing on low speed until just combined. Avoid overmixing to keep the cookies tender.
05 - Roll tablespoon-sized portions of dough into balls, flatten slightly, and arrange them 2 inches apart on the prepared baking sheets. Bake for 8 to 10 minutes until the cookies are set. Allow them to cool on the baking sheets for 2 minutes, then transfer to a wire rack to cool completely.
06 - In a mixing bowl, beat the softened butter until smooth and creamy. Add the sifted powdered sugar, heavy cream, peppermint extract, salt, and food coloring if using. Beat on medium speed until the filling is light and fluffy, about 2 minutes.
07 - Spread or pipe approximately 1 tablespoon of peppermint filling onto the flat side of half the cooled cookies. Top each with a remaining cookie, flat side down, pressing gently to form even sandwiches.
08 - Refrigerate the assembled cookies for 15 minutes to allow the filling to firm up before serving. For a festive finish, roll the edges of each sandwich in crushed peppermint candies.