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Using electric mixer, beat butter in medium bowl until light and fluffy.
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Resift flour with salt and cayenne;add to butter and beat just until blended.
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Add cheese and blend just until combined; do not overmix (dough will be crumbly).
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Gather dough into a ball; divide into fourths and flatten into disks.
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(Can be prepared ahead.Wrap and refrigerate up to 3 days or freeze up to 2 months. Thaw dough before continuing.).
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Preheat oven to 400 degrees.
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Roll 1 dough piece out between pieces of waxed paper to thickness of 1/8 inch.
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Cut out rounds using a 2 inch plain or scalloped cookie cutter.
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Repeat with remaining dough.
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Gather up scraps, reroll and cut out additional rounds.
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Transfer rounds to nonstick baking sheets (or to parchment covered regular baking sheets) and bake until golden, about 12 minutes.
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Cool slightly and serve slightly warm or at room temperature.