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Cream the butter, sugar and vanilla until very light and fluffy. Add the flour gradually, mixing until well blended (do not over mix).
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Chill dough in freezer for 30 minutes.
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Roll out a third of dough at a time, keeping remaining dough chilled.
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Onto a lightly floured board, gently roll out dough to 1/4-inch thickness. Cut with a 2-1/2-inch round cookie cutter.
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Place on an ungreased cookie sheet. Prick tops with a fork, making a pattern of 3 rows of 4 dots.
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Continue rolling out dough using scraps, mixing the warm scraps with the chilled dough.
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Bake at 350 degrees for 15 minutes until just barely browned. Cool a few minutes.
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Remove to rack to cool completely.