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In a medium bowl, combine the flour, baking powder, and salt.
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In a large bowl, with an electric mixer on medium speed, beat the butter and granulated sugar for 3 minutes, or until light and fluffy.
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Beat in the eggs, orange juice, orange peel, and orange extract.
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Beat in the flour mixture, a little at a time, until well-blended.
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Divide the dough into thirds, wrap each portion in plastic wrap, and refrigerate for 3 hours.
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Preheat the oven to 350°F and grease baking sheets or use silpats.
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Place one-third of the dough on a lightly floured surface, leaving the remaining two-thirds in the refrigerator.
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Using a floured rolling pin, roll to 1/8 inch thickness.
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Using floured cookie cutters, cut into shapes.
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Arrange on the prepared baking sheets and repeat until all the dough has been used.
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Bake for 11 minutes, or until lightly browned.
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Cool on a rack for 2 minutes- Remove to the rack to cool completely.
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(If you want, before baking and after cutting out shapes, mix 1 egg white and 2 Tablespoons water, then brush each cookie with this mixture and sprinkle on colored sugar for holidays).