Preheat oven to 375°F. Line 2 large baking sheets with parchment. Using a 2-inch round cookie cutter as a guide, trace 15-16 circles on each piece of parchment, spaced at least 1-inch apart. Turn the parchment over so the pencil marks are on the bottom. Set aside.
Prepare a piping bag fitted with a medium star tip. Set aside.
Combine the butter and powdered sugar in a medium mixing bowl. Using an electric mixer, beat until pale and fluffy. Sift the flour and cornstarch together over the butter mixture. Beat on low until just combined, then beat on medium until well blended. Scoop the mixture into the prepared piping bag.
Pipe the cookie dough into swirled rounds (not rosettes) ending in the center with a little peak. Pipe each round a little smaller than the circle. The cookies will spread a little when baking and are best when not too big. Go slow and pipe a thick stream of dough for best results.
Refrigerate the unbaked cookies for 30 minutes before baking. This will help the cookies keep their pretty shape. Repeat with remaining dough.
After 30 minutes in the refrigerator, bake the sheets, one at a time, at 375°F for 10-15 minutes. The cookies should be light golden brown around the edges. If too pale, the cookies will not hold together well when eaten. They are best when just slightly brown on the bottom. Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.