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In a small bowl, whisk together the flour, salt, and baking soda. Set aside.
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In a medium bowl, beat the butter and sugar together until light and fluffy.
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Add the egg and vanilla and beat until combined.
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Gradually add in the flour mixture, beating on low speed, until combined.
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Wrap the dough in plastic wrap and chill in the refrigerator for 1 hour.
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Preheat the oven to 350 F. Line two baking sheets with parchment paper.
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Roll out the dough to ¼-inch thickness. Cut into rounds using a 2 ½ inch round cookie cutter.
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Place cut out cookies onto prepared baking sheets and refrigerate for 15 minutes. This helps the cookies retain their shape.
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Bake the cookies for 8-15 minutes or until the edges are just starting to brown. Transfer to a wire rack to cool completely.