Preheat the oven to 300 degrees F.
Place the butter, sugar and salt in the bowl of a stand mixer with the paddle attachment and mix on medium speed until the mixture is smooth, about 2 minutes. Stop the mixer, scrape down the bowl and add all the flour at once. Turn the mixer to low speed and mix until all the flour is just combined. The dough will be crumbly at this point. Increase the mixer speed to medium and mix until the dough has completely come together.
Turn the cookie dough out onto a lightly floured surface. You can also use a large piece of parchment paper or Silpat.
Use your hands to shape the dough into a rectangle and lightly flour the top of the dough. Do not use too much flour, just enough to keep the rolling pin from sticking.
Roll the dough out to 1/2-inch thick. Use a 2-inch round cookie cutter to cut out the cookies. Place the cookies on a parchment-lined cookie sheet about 1-inch apart. Prick each cookie in the center with a fork. Pricking the cookies will ensure they bake in the center.
Reroll the cookie dough and continue to cut out cookies until all the dough has been used. You might have a small piece left over.
Chill the dough in the refrigerator for at least 20 minutes. Chilling the dough will help the cookies hold their shape when baking.
Bake the cookies for 25-30 minutes. The bottom of the cookies will be lightly golden brown.
Take the cookies out of the oven and allow them to cool for about 5 minutes on the cookie sheet before moving them to a cookie rack to completely cool.
The shortbread cookies can be stored in an airtight container for 1 week.