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In the bowl of a stand mixer with the paddle attachment, beat the butter, light brown sugar and granulated sugar together until pale and fluffy, 2 to 3 minutes. Add the egg yolk and vanilla extract; beat once more. In 2 additions, add the dry ingredient mixture, scraping down the bowl if needed, until completely combined. Transfer to the refrigerator to chill for 15 minutes.
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper and set aside.
Scoop scant tablespoonfuls of dough, roll into balls and arrange on the prepared baking sheets, spacing them a few inches apart. Make an indentation, a thumbprint, in the center of each ball of dough using your thumb and/or the help of your index finger. Bake until the bottoms are golden brown, 10 to 12 minutes. Remove from the oven and immediately reinforce the thumbprints using the end of a wooden spoon. Allow to cool completely on the baking sheets.
While the cookies are cooling, make the ganache. Place the chocolate into a heat-proof bowl. Add the heavy cream to a small saucepan set over medium-high flame and heat until the cream is scalding. Pour the cream over the chopped chocolate and allow to stand for 1 minute. Stir until smooth.