Place butter and sugar in the bowl of a stand mixer. Chill until butter is firm, about 30 minutes.Advertisement
Whisk together flour and salt; add them to the butter and sugar. Using the paddle attachment, mix on low speed until dough starts to resemble a coarse meal, about 5 minutes. Increase speed to medium and mix 2 to 3 minutes more, until dough just starts to clump around the paddle or on the sides of the bowl. Scrape the bowl and paddle; finish bringing dough together by hand.
On a lightly floured work surface, roll dough into a cylinder, then pat it into a rectangle. Lay a large sheet of parchment paper on the work surface and dust it lightly with flour. Put the dough on top. Start rolling the dough, stopping to push together any cracks that form. To keep the dough from sticking, dust the top lightly with flour and cover with another piece of parchment paper. Flip the paper-dough sandwich over. Peel off the top sheet and continue to roll until dough reaches a ¼-inch thickness (10x13-inch rectangle), repeating the flouring-flipping process as necessary. Transfer dough and parchment to a baking sheet. Cover with another piece of parchment and chill until firm, at least 20 minutes, preferably several hours or overnight.
Preheat oven to 350°. Let the dough sit at room temperature for up to 10 minutes. Invert it onto a work surface and peel off the top sheet of parchment paper. Pierce dough all over with a fork. Using a knife, pastry wheel or cookie cutters, cut dough into desired shapes. Use up remaining scraps of dough by combining and re-rolling. Arrange 12 to 16 cookies on baking sheets lined with parchment paper. Transfer to oven, lower the temperature to 325° and bake for 10 minutes. Rotate pans and bake until cookies feel firm to the touch and are lightly golden brown, 6 to 8 minutes more. Let the cookies cool completely on the pan, then store in an airtight container for up to 1 week.
Shortbread dough should be the temperature of marble--cool but not ice-cold. Start with chilled butter, refrigerate between steps and work quickly. If the dough sticks to the rolling pin or cutters, stop and transfer everything to the fridge for 10 minutes. If it cracks, let it rest at room temperature for 10 minutes. Shortbread is forgiving, but it doesn't like to be rushed.