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Preheat the oven to 375 degrees F (190 degrees C).
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In a large bowl, cream together the butter and sugar until smooth.
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Beat in the eggs, one at a time, mixing well after each.
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In a separate bowl, combine flour, baking powder, and salt; stir into the sugar mixture.
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Cover dough and chill for at least one hour.
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Roll the dough out to 1/2 inch thick and cut into desired shapes using cookie cutters.
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Place 2 inches apart on to the greased baking sheets.
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Bake for 8 to 10 minutes in the preheated oven.
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Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.
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To make frosting, mix together the confectioners' sugar, oil and 1 teaspoon vanilla until smooth.
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Gradually add enough hot water to achieve a spreadable consistency.