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Special equipment: parchment paper
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For the gluten-free flour blend: In a large bowl, whisk together the rice flour, tapioca flour, potato starch, xanthan gum and salt.
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For the cookies: In the bowl of a stand mixer fitted with the paddle attachment, beat together the butter, granulated sugar, brown sugar and vanilla on medium-high speed until light and smooth.
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Meanwhile, in a small bowl, combine the almond flour and salt with 2 cups gluten-free flour blend.
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Add to the butter mixture and beat on low speed until just combined.
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Divide the dough in half and flatten each to make 2 disks; wrap in plastic wrap and chill until slightly firm, at least 20 minutes.
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Preheat the oven to 350 degrees F and line 2 baking sheets with parchment paper.
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Working with one dough disk at a time, on a surface dusted with some gluten-free flour blend, roll out the dough to about 1/4-inch thickness.
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Using cookie cutters, cut out cookies and place on the prepared baking sheets; refrigerate until firm, about 15 minutes.
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Bake until the edges are golden, about 10 minutes.
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Let cool completely on a wire rack.
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Repeat with the remaining dough.
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For the icing: Set a wire rack over a parchment paper-lined baking sheet.
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In a small bowl, whisk together the confectioners' sugar and whipping cream until smooth.
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Submerge the cooled cookies into the icing, letting any excess drip off, then place on the prepared wire rack and decorate with sprinkles.