In the large bowl of an electric mixer, beat the butter at medium speed just until smooth, about 1 minute. Beat in the sugar and salt until well combined and slightly fluffy, scraping down the sides. Lower the speed and gradually add the flour, mixing just until thoroughly combined.
Divide the dough in half. Roll out each portion of dough between 2 sheets of waxed paper to form a circle 6 inches in diameter and 1/4 inch thick. Leave the dough between the waxed paper and transfer the circles to a baking sheet. Refrigerate until firm, at least 2 hours and up to 3 days. (You can also tuck the dough into resealable plastic bags and freeze for up to 1 month.)
Preheat the oven to 350°F (175°C) and adjust the oven rack to the center position. Line 2 baking sheets with parchment paper.
Remove 1 portion of dough from the refrigerator. Remove the top sheet of waxed paper and then place it loosely back on the dough. Turn the dough over and peel off and discard the second sheet of waxed paper.
Using the wide end of a 1/2-inch plain decorating tip (such as Ateco #6) as a cutter, cut out circles of dough. It they stick to the decorating tip, use a chopstick or wooden spoon handle to gently push through the decorating tip to release the circle of dough. Place the circles 1/2 inch apart on a baking sheet. Partially bake the cookies, 1 sheet at a time, for 6 to 8 minutes only, or until the cookies are just set. Place the baking sheet on a wire rack to cool. Repeat with the remaining dough. Reduce the oven temperature to 225°F (110°C). When the cookies have cooled to room temperature, place them on a single baking sheet lined with parchment, leaving about 1/4 inch between cookies.