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1
Place the egg yolk and vanilla in a small bowl and stir to combine; set aside.
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2
Combine the measured flour, sugar, cocoa powder, and salt in a food processor fitted with a blade attachment and pulse a few times to aerate and break up any lumps.
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3
Add the butter and pulse until the mixture looks like sand, about 25 (1-second) pulses.
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4
Add the reserved yolk mixture and pulse just until the dough forms into a ball, about 30 (1-second) pulses.
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5
Turn the dough out onto a lightly floured work surface and divide it into 2 equal portions.
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6
Using your hands and flouring them as needed, roll each portion into a log about 1 1/2 inches in diameter.
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7
Wrap each log in plastic wrap and refrigerate until just firm but still pliable, about 1 hour.
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8
(The logs will flatten slightly while chilling.
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9
If you have a paper towel tube available, cut it in half lengthwise and nestle the cookie dough in there; this will help the dough keep its cylindrical shape while it chills.)
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10
Reshape the logs so they are perfectly round and refrigerate until firm, about 1 hour more.
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11
Heat the oven to 350 degrees F and arrange the racks to divide the oven into thirds.
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12
Line 2 baking sheets with parchment paper; set aside.
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13
Remove a dough log from the refrigerator, remove the plastic wrap, and slice the dough into 1/8-inch coins.
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14
Place the cookies 1/2 inch apart on the prepared baking sheets (about 20 cookies per sheet).
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15
Place both sheets in the oven and bake for 9 minutes.
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16
Rotate the sheets front to back and top to bottom and continue baking until the edges of the cookies are firm but the tops are still soft, about 7 to 8 minutes more.
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17
Place the baking sheets on wire racks and let cool for 5 minutes.
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18
Using a flat spatula, transfer the cookies to the wire racks to cool completely.
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19
Let the baking sheets cool completely and repeat with the remaining dough (you can reuse the parchments).
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20
Place the mint candies in a resealable plastic bag.
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21
Using a meat mallet, crush them into tiny pieces, but dont totally pulverize them into a powder.
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22
(Alternatively, you can use a frying pan to crush the candies.)
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23
You should have about 1/3 cup; set aside.
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24
Combine the powdered sugar and butter in the bowl of a stand mixer fitted with a paddle attachment and mix on low speed until crumbly, about 2 minutes.
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25
Gradually increase the speed to medium and beat until smooth, about 2 minutes more.
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26
Add the vanilla and beat until smooth, about 1 minute.
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27
Stop the mixer and scrape down the paddle and the sides of the bowl with a rubber spatula.
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28
Increase the speed to high, add the crushed candies, and beat until just combined, about 10 seconds.
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29
Place the filling in a large resealable plastic bag, push to one bottom corner, and cut a 1/2-inch opening in that corner.
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30
Flip half of the cooled cookies onto their tops, and pipe the filling (about a heaping teaspoon) onto each cookie bottom.
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31
Close with the cookie tops and gently press to flatten until the filling reaches the edges.
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32
Store in an airtight container at room temperature for up to 3 days.
