Preheat oven to 300 degrees. Whisk together flour and salt in a bowl. In another bowl, beat butter on medium-high speed until fluffy, 3 to 5 minutes. Gradually add sugar, beating until combined; continue to beat until mixture is very pale, about 2 minutes more. Reduce speed to low; beat in flour mixture.
Place dough on a piece of parchment and shape into a rectangle. Top with a piece of plastic wrap and roll out slightly less than 1/4 inch thick. Trim to a 10-by-12-inch rectangle. Transfer dough and parchment to a baking sheet. Refrigerate until firm, about 20 minutes. Cut into quarters lengthwise, then crosswise into quarters to create smaller rectangles. Cut rectangles on diagonal, creating triangles. Pierce all over with a skewer.
Bake until firm in centers and golden brown, 45 to 50 minutes. Transfer sheet to a wire rack; immediately recut triangles with a paring knife. Let cool completely. Shortbread can be stored up to 1 week.