Whisk together flour, sugar, and salt in a bowl.
Place butter into the bowl of an electric mixer fitted with the paddle attachment. Beat on medium-high speed until fluffy, 3 to 5 minutes, scraping down sides of the bowl.
Gradually add flour mixture; beat until pale and fluffy, about 2 minutes.
Press dough into a parchment paper lined 9x9 pan. Place a sheet of plastic wrap on the dough, refrigerate 20 minutes.
Preheat oven to 300 degrees, with rack in upper third.
Remove plastic wrap. Cut dough into desired shapes with a knife. Using a toothpick or wooden skewer, prick all over at 1/4-inch intervals.
Bake until golden brown and firm in the center, about 45 minutes to 1 hour. Remove pan to a wire rack.
Recut shortbread into previous shapes; let cool completely.
Remove using the parchment as handles and transfer shortbread to an airtight container.