Beat the butter and confectioners' sugar with an electric mixer until light and fluffy, 2 to 3 minutes. Beat in the vanilla extract and egg yolks until combined. Turn the mixer down to its slowest setting and gradually add the flour mixture and dark chocolate. Mix until just combined.
Divide the dough in half, flatten into two disks and wrap in plastic wrap. Chill in the refrigerator for at least 1 hour or up to a couple days.
Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
Between two lightly floured pieces of parchment paper, roll out the first disk of dough to approximately 3/8-inch thick. (If the dough cracks while rolling out, allow it to warm up for 10 minutes or so, and then continue rolling. It rolls out best when cool, but not overly cold.) Cut into 2-inch rounds, and then place on the prepared baking sheets. Gather the dough scraps, press into a disk shape and place in the fridge. Repeat with the second disk of dough (and then the scraps), until all of the dough is rolled and cut.
Bake until the cookies are set and no longer glossy, 8 to 10 minutes. Allow to cool for a few minutes on the baking sheets, and then carefully transfer to wire racks to finish cooling.
For the peppermint cream filling: Whisk together the confectioners' sugar, butter, cream and peppermint extract until smooth.
Spread about 1 heaping teaspoon of the filling on one cookie, top with a second cookie and gently press together. Repeat with the remaining cookies and filling. Dust with confectioners' sugar if desired.