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Cream butter and sugar until fluffy; add egg and beat well.
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In a separate bowl, combine flour, baking powder and salt. Gradually add this dry mixture to the creamed mixture.
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Cover and chill at least 6-8 hours (or overnight).
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Preheat oven to 350°F Lightly grease cookie sheets.
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Roll cookies out thin, into a large rectangle, about 1/8-inch thin.
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Using a butter knife, run columns down and then across to make squares approx 2" to 2 1/2" squared. Place on greased cookie sheets.
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Combine 1/3 cup sugar and the 1 tsp cinnamon and mix well; set aside.
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Brush tops of cookies with egg white wash. Sprinkle with cinnamon/ sugar mixture.
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Place a pecan half in the center of each square.
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Bake at 350°F for approximately 8 minutes, or until just SLIGHTLY getting golden-brown at edges.
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Cool completely; store in airtight container.