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In a large bowl, beat butter, sugar and vanilla with electric mixer at medium speed until light and fluffy.
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With wooden spoon, stir in milk and flour; then mix by hand until dough is smooth.
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Divide dough into two parts.
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Preheat oven to 325 degrees.
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On a lightly sugared pastry cloth, roll out dough, one part at a time, into an 8-inch circle, 1/4 inch thick.
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Place a 4-inch saucer in the center; cut around it.
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Remove saucer and flute outside edge as for a pie shell.
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Cut outer ring into eight sections.
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Keep center whole.
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Prick all over with fork.
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Place 1 inch apart on ungreased cocokie sheet.
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Bake 25- 30 minutes, or until light golden.
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Cool completely on wire rack.
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Makes 2 shortbreads.