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Stir together flour, ginger, baking soda and salt; set aside.
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In a large bowl, cream shortening and sugar until fluffy.
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Add molasses, egg, and extract; beat well.
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Stir in flour mixture until well blended.
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Wrap airtight.
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Chill overnight or at least 2 hours until firm enough to roll.
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Cut dough in thirds; roll out each third (keeping remainder in refrigerator) on lightly floured pastry cloth or other surface about 1/8-inch thick.
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Cut into shapes with cookie cutters.
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With spatula, transfer to lightly greased baking sheet, keeping cookies 1/4-inch apart.
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Repeat with remainder of dough and scraps.
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Bake in preheated 375 F oven for 6-7 minutes or until light brown.
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Remove to racks to cool.
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Frost when cool.
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Store airtight in cool place.
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(Can be used for Christmas ornaments by making a small hole near the top of each cookie with a toothpick before baking.).