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Beat together butter and sugar in a large mixing bowl until light and fluffy, about 2 minutes. Add egg and vanilla, mix to combine.
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In a medium bowl, mix flour and salt. Add flour mixture to butter mixture, mix until just combined.
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Wrap the cookie dough in plastic wrap. Refrigerate for at least 3 hours.
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Preheat oven to 375 degrees F. Line a baking sheets with a Sil-Pat or parchment paper; set aside.
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Roll out dough to 1/4" thick, and cut into 3" rounds. Transfer cookie dough rounds to prepared baking sheets.
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In a small bowl, beat egg whites with a fork. Use a pastry brush to coat the top of each cookie round with egg white. In another small bowl, combine 2 tablespoons sugar and cinnamon. Sprinkle cinnamon sugar over top of cookies.
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Bake for 10 to 12 minutes. Remove from oven and cool for 1 minute on baking sheet. Transfer cookies to wire rack to cool completely.