Using a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter with the sugar and salt. Add the vanilla extract and beat to combine. Add the flour and espresso powder and mix on low speed until combined.
Transfer the dough onto a piece of parchment paper or plastic wrap and roll into a log, twisting the ends so that it's tightly wrapped. Chill in the refrigerator for at least 2 hours.
Preheat the oven to 350°F, keeping the dough in the refrigerator until the oven is ready to use. Line baking sheets with parchment paper and set aside.
Remove the dough from the refrigerator, unwrap, and slice into ½ inch rounds. Arrange on prepared baking sheets, 2 inches apart, and and bake for 18-20 minutes. Allow the cookies to cool on baking sheet for 10 minutes, then transfer to a cooling rack to cool completely.
For me, the recipe yields just about 24 cookies but this can vary slightly based on how thick or thin you slice your cookies.
For perfectly round and uniform cookies, I like to use a round cookie cutter when the cookies are still warm and soft, to further reinforce the round shape. Do not attempt to pull the cut cookies off until they have cooled.