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1
Put oven racks in upper and lower thirds of oven and preheat oven to 350u00b0F. Butter 2 large baking sheets.
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2
Whisk together flour, baking soda, and salt in a bowl. Stir together buttermilk and vanilla in a cup.
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3
Beat together butter and sugar in a large bowl with an electric mixer at medium-high until pale and fluffy, about 3 minutes, then add egg, beating until combined well. Reduce speed to low and add flour mixture and buttermilk mixture alternately in batches, beginning and ending with flour mixture, and mixing just until smooth.
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4
Drop rounded teaspoons of batter 1 inch apart onto baking sheets. Bake, switching position of sheets halfway through baking, until tops are puffed, edges are pale golden, and cookies spring back when touched, 6 to 8 minutes total. Transfer to a rack to cool.
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5
Stir together confectioners sugar, corn syrup, lemon juice, vanilla, and 2 tablespoons water in a small bowl until smooth. If icing is not easily spreadable, add more water, 1/2 teaspoon at a time. Transfer half of icing to another bowl and stir in cocoa, adding more water, 1/2 teaspoon at a time, to thin to same consistency as vanilla icing. Cover surface with a dampened paper towel, then cover bowl with plastic wrap.
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6
With offset spatula, spread white icing over half of flat side of each cookie. Starting with cookies you iced first, spread chocolate icing over other half.
