Lemon-Glazed Pistachio Shortbread Cookies

Preheat the oven to 350 °F. Line 2 baking sheets with parchment paper. In a medium bowl, whisk together the flour, cornstarch, and salt. Working with a stand mixer, preferably fitted with the paddle attachment, or with a hand mixer with a large bowl, beat the butter and 1 cup of the confectioners' sugar on medium speed until smooth. With the mixer on low speed, gradually mix in the flour mixture until just combined and it holds together when squeezed (it will be slightly crumbly). Stir in the pistachios. Gather the dough into a disk. On a lightly floured surface, roll the dough out to a generous 1/4 inch thick. Cut into rounds with a 1 1/2-inch cookie cutter and place 2 inches apart onto the prepared baking sheets, rerolling and cutting the scraps as necessary. Refrigerate until firm, about 30 minutes. Bake until the edges are set and light golden brown, 12 to 15 minutes. Transfer to a wire rack and let cool completely. Meanwhile, in a medium bowl, whisk together the remaining 1 1/2 cups confectioners' sugar, lemon zest, and lemon juice until smooth. Place the wire rack over a baking sheet to catch any drips. Dip the tops of the cookies into the glaze and place on the rack. Let set for 15 minutes.