Sift flour, 3/4 cup powdered sugar, cornstarch, and salt into medium bowl. Using electric mixer, beat butter in large bowl until fluffy. Gradually beat in granulated sugar and vanilla. Stir in dry ingredients in 3 additions, mixing until just blended each time. Gather dough into ball; divide in half. Roll each half into 6-inch-long log; wrap each log in plastic wrap and refrigerate at least 2 hours or overnight.
Position racks in top third and center of oven; preheat to 325°F. Cut each log crosswise into 1/3-inch-thick slices. Arrange slices on 2 heavy large baking sheets, spacing 1/2 inch apart (cookies will spread very little). Bake cookies 9 minutes. Reverse baking sheets; bake just until cookies turn golden brown at edges, about 9 minutes longer. Cool cookies on sheets 1 minute. Using thin metal spatula, transfer cookies to racks; cool.
Optional: Roll in granulated sugar, powdered sugar or vanilla sugar
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