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