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Place the shortening and sugar into a mixing bowl and rub or beat with a spoon until the mixture is light and fluffy.
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Add the egg and the molasses and beat well.
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Sift flour before measuring, then sift again with the dry ingredients so that they are mixing well.
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Add the flour mixture to the shortening mixture and mix well.
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Refrigerate the dough for at least 1 hour.
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Preheat the oven to 375°F.
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Shape the dough into 1-inch balls.
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Roll each ball in granulated sugar.
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Place the balls 2-inches apart on an ungreased cookie sheet.
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Bake the cookies at 375° for 8-10 minutes or until lightly browned.
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Remove from the oven and allow them to cool slightly (about 2 minutes).
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Remove from the cookie sheet to wire racks to cool completely.