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In a large mixing bowl, beat butter with electric mixer 30 seconds.
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Add sugar, baking powder and salt. Beat until combined.
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Beat in the egg and vanilla until combined.
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Beat in as much of the flour as you can with the mixer.
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Stir in any remaining flour with wooden spoon.
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Divide dough in half.
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Mix coffee powder and water; knead into one portion of dough.
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Shape each dough portion into rectangular 6 x 2 inch log.
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Wrap logs in waxed paper or plastic wrap; chill 1 hour.
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With a sharp knife, cut each log lengthwise into four slices.
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Alternating colors, stack slices to form two four-layer logs.
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Press together to seal layers.
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Wrap logs in paper or plastic wrap, and chill 30 to 60 minutes, or until firm.
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Place logs on a cutting surface with the solid color facing up.
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Using a sharp knife, cut each log lengthwise into four slices. (Each will have four layers in alternating colors.)
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Stack four slices of dough, alternating colors for a checkerboard effect.
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Repeat with remaining slices for second log.
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Trim edges to straighten.
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Wrap and chill for 1 to 2 hours, or until firm.
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Cut each log crosswise into 1/2-inch-thick slices.
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Place slices 2 inches apart on ungreased cookie sheets.
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Bake in a 375F oven for 10 to 12 minutes, or until edges are lightly browned.
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Transfer cookies to wire racks and let cool.