Whisk together flour, cornstarch, and salt in a bowl.
Beat together butter and sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 2 minutes in a stand mixer or 4 minutes with a handheld. Reduce speed to low, then add zest and vanilla and mix until combined.
Add flour mixture and mix until al soft dough forms. Gather dough into a ball and wrap in plastic wrap, then flatten (in wrap) into a 7" disk. Chill until firm, at least 4 and up to 24 hours.
Bring dough to cool room temperature before rolling out, about 1 hour.
Put oven rack in middle position and preheat oven to 400°F.
Roll out dough into a 14" round (1/4" thick) on a well-floured surface with a lightly foured rolling pin. Cut out as many cookies as possible with cutter (2" fluted or plain round cookie cutter) and transfer with a metal spatula to 2 ungreased large baking sheets, arranging cookies about 1" apart. Bake cookies, 1 sheet at a time, until pale golden, 10-12 minutes. Manwhile, gather scraps into a ball, then flatten into a disk, and chill while first batch bakes. Transfer baked cookies to a rack to cool.
Reroll scraps and cut out additional cookies, transferring to a cooled cookie sheet as formed, then bake in same manner.