How to Make It
Sift together flour, cocoa, salt, and baking powder in a medium bowl; set aside. Beat butter, sugar, and espresso in the bowl of a stand mixer fitted with the paddle attachment on medium speed until light and fluffy, about 4 minutes. With mixer running, add egg, beating until well combined. Stir in vanilla. Gradually add flour mixture, beating on low speed until just combined, about 30 seconds. Wrap dough in plastic wrap, and chill until firm, at least 2 hours or up to 3 days.
Preheat oven to 350°F. Roll dough out on a parchment paper–lined work surface into a large (14- x 11-inch) rectangle (about 1/8 inch thick), flouring top of dough as needed to prevent sticking. Trim into a 13- x 10-inch rectangle, discarding scraps. Slide parchment paper with dough rectangle onto a large baking sheet. Chill until firm, about 30 minutes. Using the blunt end of a wooden skewer, prick holes all over dough about 3/4 inch apart. Bake in preheated oven until set in middle but still soft, 9 to 11 minutes. Transfer baking sheet to a wire rack, and let cookie cool completely, about 30 minutes.
Cut cookie crosswise into 2 rectangles. Invert 1 cookie half onto a large piece of aluminum foil; top with ice cream, spreading to edges in an even layer. Place (do not invert) remaining cookie half on top of ice cream. Wrap in aluminum foil, and freeze 8 hours.
Remove frozen sandwich from foil; trim edges, if desired. Cut into 12 bars. Serve immediately.