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Preheat the oven to 350°.
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Line a baking sheet with parchment paper.
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In a medium bowl, sift together the flour, cocoa, baking soda and salt.
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Using a mixer, beat 5 tablespoons butter with the granulated sugar until fluffy, 3 minutes.
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Beat in the egg, food coloring and 1 teaspoon vanilla.
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Beat in the flour mixture alternately with the buttermilk until smooth.
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Place 1/4-cup scoops of batter 2 inches apart on the prepared baking sheet; spread out.
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Bake until a toothpick inserted in the center comes out dry, 12 to 15 minutes.
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Let the cookies sit for 5 minutes, then transfer to a rack to cool.
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In a bowl, whisk together the confectioners' sugar, remaining 1/2 teaspoon vanilla, 1 tablespoon corn syrup and 2 tablespoons hot water until smooth.
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In another bowl, combine the chocolate, remaining 3 tablespoons butter and 1 tablespoon corn syrup; microwave until melted, about 1 minute.
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Coat the cookies with the vanilla, then the chocolate icing.
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Refrigerate until set, about 20 minutes.