In a medium bowl, whisk together the flour, cocoa powder, espresso powder, baking powder, and salt. Set aside.

In a large bowl using a handheld or a stand mixer fitted with a paddle attachment, beat the butter and sugar together on medium-high speed until smooth and creamy, about 3 minutes. Add the egg and vanilla and beat on medium-high speed until combined, about 1 minute. Scrape down the sides and bottom of the bowl and beat again as needed to combine.

Add the dry ingredients to the wet ingredients and mix on low speed until combined. The dough will be soft and sticky. Cover the bowl tightly and refrigerate for at least 1 hour and up to 2 days.

Line large baking sheets with parchment paper or silicone baking mats. Scoop a heaping Tablespoon (about 30g) of chilled cookie dough per cookie and roll into balls. Arrange dough balls 3 inches apart on the prepared baking sheets. Place the cookie stamp directly on top of each cookie dough ball, centering it as best as you can, then firmly press down until the dough extends nearly to the edges of the cookie stamp. Lift straight up. If your cookie dough is sticking to the cookie stamp, use a pastry brush to lightly brush cocoa powder on the stamp before stamping the cookie dough ball. You can then brush the excess cocoa powder off the tops of the stamped cookies, if desired.

Chill the stamped cookies in the refrigerator for 1 hour before baking.

Preheat the oven to 350°F (177°C).

Bake the cookies until the edges are set, about 11–13 minutes. Remove from the oven and allow the cookies to cool on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely.

Using a fork or small whisk, mix the espresso powder and warm water together in a medium bowl until dissolved. Whisk in the confectioners’ sugar and milk/cream. For thinner glaze, whisk in more milk. For thicker glaze, whisk in more confectioners’ sugar. Using a pastry brush, brush the glaze on top of the cookies (or you can dip the tops of the cookies in the glaze). The glaze sets on the cookies in about 1 hour.

Cover leftover cookies tightly and store at room temperature for up to 1 week.