Preheat the oven to 350°F / 175°C. Line two baking sheets with parchment paper.
Fill the bottom of a double boiler or a medium saucepan with 1 inch / 2.5cm of water and bring to a gentle simmer over medium-low heat. In a large stainless steel bowl over the double boiler, melt half (6 oz / 175g) of the chopped chocolate with the butter and stir until smooth. Remove from the heat.
In a stand mixer fitted with the whisk attachment, beat the eggs, sugar, and vanilla until light and foamy, about 5 minutes.
In a small bowl, whisk the flour, baking powder, and salt.
Stir the flour mixture into the melted chocolate. Fold the chocolate mixture into the whipped eggs along with the remaining 6 oz / 175g chopped chocolate.
Let the mixture sit for 10 minutes to allow the chocolate to set firm.
Scoop the cookie dough using a #70 (2½-teaspoon) portion scoop onto the prepared baking sheets, leaving about 3 inches between them. You can make the cookies larger or smaller, but it will affect the baking time.
Bake, one sheet at a time, in the middle of the oven for about 8 minutes, until the tops are puffed and just start to crack. Take care to not overbake them.
Allow the cookies to cool completely before peeling them off the parchment paper to fill them.
Make the mint buttercream: In a medium bowl, mix the butter and confectioners' sugar with a wooden spoon or handheld mixer until smooth and fluffy. Add the mint extract to taste.
Spread the buttercream onto half of the cookies and then top with the remaining cookies.
Dip the edges in the crushed candy cane.
Cover and refrigerate until you are ready to serve. These can also be made a day ahead.
