In a medium bowl, whisk the flour with the cornstarch. In a stand mixer fitted with the paddle, cream the butter with the confectioners' sugar and salt at medium speed for 2 minutes. Add the flour mixture all at once and mix at low speed just until incorporated. Pat the dough into an 8-inch disk, wrap in plastic and refrigerate until just firm, about 15 minutes.
Roll out the dough between 2 sheets of parchment paper to a 1/4-inch-thick round. Slide the dough onto the parchment, onto a baking sheet and refrigerate until firm, about 15 minutes.
Preheat the oven to 325°. Line 2 baking sheets with parchment paper. Slide the dough onto a work surface. Peel the top sheet of parchment off the dough. Prick the dough all over with a fork. Using a 2-inch fluted round cookie cutter, stamp out cookies as close together as possible. Arrange the cookies 1 inch apart on the prepared baking sheets. Refrigerate the cookies. Reroll the scraps between sheets of parchment paper and refrigerate until firm. Stamp out more cookies and arrange them on the baking sheets.
Bake the cookies on the upper and middle racks of the oven for 30 minutes. Reduce the oven temperature to 250°. Shift the sheets from top to bottom and back to front and bake for 15 minutes longer, until golden brown. Let the cookies cool on the sheets for 2 minutes, then transfer them to a rack.
Put the granulated sugar in a shallow bowl. Carefully toss the warm cookies in the sugar to coat, then let cool completely on the rack before serving.