For the dough to have the proper consistency when rolling, make sure to use cold butter directly from the refrigerator. In step 3, use a rolling pin and a combination of rolling and a pushing or smearing motion to form the soft dough into an oval. A rimless cookie sheet helps achieve evenly baked cookies; if you do not have one, use an overturned rimmed baking sheet. Dough scraps can be combined and rerolled once, though the cookies will be slightly less tender. When the cookies are ready to come out of the oven, they will show slight resistance when gently pressed. If they yield easily, they are underdone and need more time to crisp; if they begin to darken at the edges, they have baked too long and will taste burnt and bitter. If desired, stir 1 or 2 drops of food coloring into the icing. For a pourable icing, whisk in milk, 1 teaspoon at a time, until the desired consistency is reached. You can also decorate the shapes with sanding sugar or sprinkles before baking.
1. FOR THE COOKIES: Whisk egg, espresso powder, salt, and vanilla together in small bowl. Whisk flour, cocoa, baking powder, and baking soda together in second bowl.
2. Process sugar in food processor until finely ground, about 30 seconds. Add butter and process until uniform mass forms and no large pieces of butter are visible, about 30 seconds, scraping down sides of bowl as needed. Add egg mixture and process until smooth and paste-like, about 10 seconds. Add flour mixture and process until no dry flour remains but mixture remains crumbly, about 30 seconds, scraping down sides of bowl as needed.
3. Turn out dough onto counter; knead gently by hand until smooth, about 10 seconds. Divide dough in half. Place 1 piece of dough in center of large sheet of parchment paper and press into 7 by 9-inch oval. Place second large sheet of parchment over dough and roll dough into 10 by 14-inch oval of even ⅛-inch thickness. Transfer dough with parchment to rimmed baking sheet. Repeat pressing and rolling with second piece of dough, then stack on top of first piece on sheet. Refrigerate until dough is firm, at least 1 1/2 hours (or freeze for 30 minutes). (Rolled dough can be wrapped in plastic wrap and refrigerated for up to 5 days.)
4. Adjust oven rack to lower-middle position and heat oven to 300 degrees. Line rimless cookie sheet with parchment. Working with 1 piece of rolled dough, gently peel off top layer of parchment. Replace parchment, loosely covering dough. (Peeling off parchment and then returning it will make cutting and removing cookies easier.) Turn over dough and parchment and gently peel off and discard second piece of parchment. Using cookie cutter, cut dough into shapes. Transfer shapes to prepared cookie sheet, spacing them about 1/2 inch apart. Bake until cookies show slight resistance to touch, 14 to 17 minutes, rotating sheet halfway through baking. Let cookies cool on sheet for 5 minutes. Using wide metal spatula, transfer cookies to wire rack and let cool completely. Repeat cutting and baking with remaining dough. (Dough scraps can be patted together, rerolled, and chilled once before baking.)
5. FOR THE ROYAL ICING: Using stand mixer fitted with whisk attachment, whip all ingredients on medium-low speed until combined, about 1 minute. Increase speed to medium-high and whip until glossy, soft peaks form, 3 to 4 minutes, scraping down bowl as needed.
6. Spread icing onto cooled cookies. Let icing dry completely, about 1½ hours, before serving.