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Preheat the oven to 350 degrees.
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Sift the flour, baking soda, cream of tartar, and salt together into a medium bowl. Set aside; these are your dry ingredients.
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Combine the butter and vanilla in a large bowl and beat with an electric mixer until very smooth.
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With mixer on medium, gradually beat in the granulated sugar. Continue beating until very light and fluffy (several minutes), scraping down the bowl as necessary.
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Beat in the egg yolks one at a time, beating well after each addition.
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Turn mixer to low and gradually beat in the dry ingredients until a cohesive dough forms. Stir a few times with a rubber spatula to ensure everything is mixed well.
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Roll tablespoons of dough into balls and arrange 2 inches apart on un-greased unlined baking sheets.
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Bake 12 to 18 minutes, until the cookies are cracked all over the tops.
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Cool on baking sheets for 1 minute, then carefully transfer to wire racks to cool completely before frosting them.