In a large bowl, with a hand mixer on medium speed, mix the butter and powdered sugar until it reaches a creamy consistency.
Add the vanilla extract, all-purpose flour, and salt. Continue mixing until combined; the mixture will be crumbly.
Using your hands, shape the dough into a ball then roll it out into a log shape, approximately 2 inches in diameter and 12 inches in length. Wrap tightly in plastic wrap and refrigerate for at least 1 hour, up to overnight.
Preheat the oven to 400°F. Line 2 baking sheets with parchment paper.
Remove from refrigerator and set dough onto a flat work surface. Slice the dough into 1/8-inch rounds. Arrange onto the prepared baking sheets, spacing the cookies at least 1 inch apart.
Bake for 8 minutes, until the edges are lightly golden. Remove from the oven and let the cookies rest for 1 minute on the baking sheet, then transfer to a wire rack to cool completely and serve.