Thin as they may be, these cookies pack an intense coffee flavor.
Sift flour, cocoa powder, espresso, and salt into a bowl; set aside. Put butter, sugar, and vanilla into the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until pale and fluffy. Reduce speed to low. Gradually mix in flour mixture.
Divide dough in half. Place each half on a piece of parchment paper, and shape dough into rough logs. Fold parchment over dough; using a ruler, roll and press into a tight log. Wrap in parchment. Chill in freezer until hard, about 30 minutes (up to 2 weeks).
Preheat oven to 350. Unwrap logs; cut into 1/8-inch-thick rounds, and space 1 1/2 inches apart on parchment-lined baking sheets. Bake until firm, 20 to 25 minutes. Transfer cookies to wire racks; let cool completely.
Cookies can be stored in airtight containers up to 2 weeks.