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Place the oven rack to the middle position.
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Preheat the oven to 350 degrees F.
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Line two baking sheets with parchment paper.
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In a medium bowl, combine the flour, cocoa powder (I prefer natural cocoa rather than sweetened), baking soda and salt.
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In the bowl of a stand mixer fitted with a paddle, beat the butter on medium until smooth.
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Add the 1¾ cups sugar and beat on medium until light and fluffy. This should take about 2-3 minutes to arrive at the "fluffy" light yellow look.
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Add the egg and vanilla and beat on medium until combined.
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Add the flour mixture and beat on low until just combined.
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Place the remaining 1 cup sugar in a medium bowl. Stir in cardamom, if desired.
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Form the cookies into balls. The original recipe recommends about ⅓ cup dough for each cookie. I made mine smaller (about 2T).
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Roll each ball in the sugar and place cookies on each prepared sheet pan. Bake one sheet at a time 11 to 14 minutes, until the edges have set and the centers are puffed and starting to crackle. I cooked mine for about 11 minutes. Mine were smaller than the recipe called for though, so cooking time was on the shorter side.
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Transfer the baking sheet to a wire rack and let the cookies cool completely on the pan.