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Using a stand mixer, cream the butter and sugar for about 1 minute on medium speed.
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Mix in egg and vanilla. Scrape down the sides as needed. Set aside.
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In a medium-sized bowl, whisk together the flour, salt, baking powder, baking soda, and cream of tartar.
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With the mixer running on low speed, slowly add the dry ingredients to the wet ingredients until well blended.
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The dough should be quite thick, and you may have to stir the rest by hand.
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Add the food coloring, and mix until well combined.
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Roll the dough into balls, and then roll into the blue sanding sugar.
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Preheat oven to 350 Fahrenheit. Line two large baking sheets with parchment paper.
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Bake in the oven for 8–10 minutes.
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Once baked, allow cookies to cool for 1 minute before placing rock candy in the center.