Fit a square of parchment to the bottom of a 9-inch (23-cm) square pan. You can butter the bottom of the pan to help the square of parchment adhere to the pan, if necessary. Preheat the oven to 350 ºF (175 °C).
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter, sugar, and salt until it is smooth, light, and creamy. This takes 3–4 minutes. Scrape down the sides of the bowl with a spatula to make sure the ingredients combine properly.
Add the flour to the mixer bowl and mix it in until the mixture turns into a sandy crumble that holds together when pressed.
Spread the crumbly mixture evenly from edge to edge on the bottom of the prepared pan. Pat it out and press it down using a flat-bottomed glass to smooth it.
Cut the shortbread into 24 rectangles, and dock it with a fork. Bake for 35–40 minutes until the edges turn golden brown.
Let the pan of shortbread cool for 5 minutes, then cut them again. Let them cool 10 minutes before unmolding.
Let cool before serving.
Notes
You can bake the shortbread a second time to ensure that even the very middle parts are baked through, yielding a buttery yet dry shortbread with a sandy texture, as it should be. Transfer the shortbread to a parchment-lined baking sheet, 1 inch apart, and bake at 325 ºF for another 10–20 minutes or so until they are baked through.
Another option for making properly baked shortbread that aren't overly brown but still baked through: bake the shortbread at a lower temperature. Try baking shortbread at 300ºF for longer. Low and slow is the key to achieving perfectly baked shortbread that are evenly golden brown.