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1
In a microwave-safe bowl, melt the bittersweet and mint chocolates in 30-second intervals until nearly melted.
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2
Whisk until smooth, then let cool.
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3
In a medium bowl, whisk the flour with the cocoa and salt.
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4
In the bowl of a standing electric mixer fitted with the paddle, beat the butter until creamy.
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5
Add the granulated sugar and brown sugar and beat at medium-high speed until light and fluffy, about 3 minutes.
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6
Beat in the egg yolks and vanilla.
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7
Scrape the chocolate into the mixer and beat just until incorporated.
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8
Add the dry ingredients and beat at low speed, scraping the side of the bowl occasionally, until smooth.
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9
Transfer the dough to a sheet of plastic wrap and pat it into a 7-inch disk; wrap it up and refrigerate until chilled and firm, at least 1 hour.
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10
Preheat the oven to 350 and position racks in the upper and lower thirds.
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11
Line 2 cookie sheets with parchment paper.
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12
Spread the coarse sugar in a shallow bowl.
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13
Scoop up tablespoons of the dough and roll them into balls, then roll in the coarse sugar; transfer to the baking sheets.
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14
Using your thumb or a melon baller, make an indentation in the center of each cookie.
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15
Bake the cookies for 10 minutes, until slightly firm.
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16
Remove the cookie sheets from the oven.
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17
Using the melon baller, press into the cookies again.
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18
Return the cookies to the oven, shifting the cookie sheets, and bake for 5 minutes longer, just until dry but not hard.
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19
Transfer the cookie sheets to racks to cool completely.
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20
Put the white chocolate in a heatproof cup.
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21
Put the cream into a microwave-safe bowl and microwave at high power until boiling, about 30 seconds.
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22
Pour the hot cream over the white chocolate and let stand until melted, then whisk until smooth.
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23
Stir in the peppermint extract.
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24
Fill the thumbprints with the white-chocolate ganache and refrigerate just until set, about 30 minutes.
