The secret to the super-crisp texture here is cutting the dough into very thin rounds; coarse sanding sugar on top adds to their crunch.
Sift together flour, cocoa powder, espresso powder, and salt into a medium bowl; set aside.
Put butter, confectioners sugar, zest, and vanilla in the bowl of an electric mixer. Mix on medium speed until pale and fluffy, 3 minutes. Reduce speed to medium-low; gradually add flour mixture.
Transfer dough to a 12-by-16-inch piece of parchment paper; shape into a log. Roll in parchment to 1 1/2 inches in diameter, pressing a ruler along edge of parchment at each turn to narrow log and force out air. Transfer dough log in parchment to a paper-towel tube; refrigerate 2 hours (or overnight).
Preheat oven to 350 degrees. Cut log into 1/4-inch-thick slices; transfer to parchmentlined baking sheets. Brush tops with water; sprinkle with sanding sugar.
Bake until set, 15 to 17 minutes. Let cool on sheets on wire racks.