Preheat oven to 325 degrees and line a baking sheet with parchment paper or a silicon mat.

Add the chocolate and shortening to a medium-sized microwave safe bowl and heat on 50% power for 30 seconds. Stir well and continue to heat at 50% power for 15 second intervals (stirring each time) until the chocolate is melted. Stir in the sugar and then add the eggs and vanilla mix until combined.

In a large bowl, sift and whisk together the flour, xanthan gum, cocoa powder, baking soda, baking powder, and salt. Pour the chocolate mixture into the dry ingredients and mix until combined - the dough will be stiff. Use your hands to knead the dough to bring it together.

Roll the dough out between 2 pieces of parchment paper until it is 1/8-1/4 inch thick. Carefully transfer the dough (still on the parchment paper) onto a baking sheet and freeze for 5 minutes. Use a 2-inch round cookie cutter to cut the cookies and place the cut cookies on the prepared baking sheet, placing them 1 inch apart. Bake the cookies in batches for 15 minutes. Cool completely on a wire rack before adding the filling.

Cream together the butter and shortening in the bowl of a stand mixer until combined. Add the powdered sugar, meringue powder, and salt and mix on low speed until incorporated. Increase the mixer speed to medium and beat until fluffy, about 1 minute.

Add the milk, vanilla, and peppermint extract and beat an additional minute.

To assemble, spread the filling on a cookie and then top with another cookie. Sprinkle crushed candy cane pieces around the sides of the filling and gently press on to adhere. Serve immediately or keep in an air-tight container until ready to serve.