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Preheat the oven to 350 degrees.
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Sift the flour, cornstarch, baking soda, and salt together into a medium bowl. Set aside; these are your dry ingredients.
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Combine the butter, vanilla, and nutmeg 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 (this will take several minutes). Scrape down the sides and the bowl as necessary.
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Beat in the egg yolks one at a time, then beat in the eggnog.
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Turn mixer to low and gradually mix the dry ingredients into the butter-eggnog mixture; continue beating until a cohesive dough forms. Stir a few times with a spatula to ensure everything is fully combined.
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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 10 to 15 minutes, until the cookies are cracked on top and have mostly flattened out.
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Cool the cookies on baking sheets for 1 minute, then carefully transfer to wire racks to cool completely before frosting them. (A thin metal spatula is helpful.)