Preheat oven to 325°F. Line two baking sheets with parchment paper.
Beat butter, powdered sugar, granulated sugar, and lemon zest until pale and creamy, about 2 minutes.
Mix in lemon juice and vanilla until fully combined.
Whisk flour, cornstarch, and salt. Add to the bowl and mix on low just to form a soft dough.
Chill the dough 20 minutes to firm up for easier shaping.
Roll to about 1/4 inch thick or press into a slab. Cut shapes and place 1 inch apart.
Sprinkle lightly with sugar. Prick each cookie once with a fork for even baking.
Bake 14 to 16 minutes until set and edges are barely golden. Rotate pans halfway.
Cool 5 minutes on the sheets, then transfer to a rack to finish cooling.