Step 1

In a food processor, pulse the flour, powdered sugar, cocoa powder and salt until combined.With the processor running, drop in the pieces of butter, one at a time. Pulse a few times until evenly distributed.Add the vanilla and milk. Process just until the dough comes together and sticks together in a ball.

Step 2

Note that if you don't have a food processor, you can make the dough in a bowl, using a pastry cutter to cut the butter into the flour mixture. Then use your hands to work in the liquid until it comes together into a dough.

Step 3

Turn the dough out, and knead a few times, just to fold in any floury bits. Shape the dough into a disk, wrap in plastic, and refrigerate for 20 minutes.

Step 4

Divide the dough into 12 equal portions. They should be as close in size as possible, so it's helpful if you have a food scale, to weigh the dough, then weigh each portion so they're uniform in size.Roll each portion between your hands to shape a ball, and lightly dust each ball of dough in flour.Place the dough balls on a baking sheet lined with parchment paper.

Step 5

Dip a cookie stamp in flour, then tap off the excess. Center the stamp over a ball of dough, then firmly press down on the dough, until it flattens and spreads out all the way to the edge of the stamp. Carefully pull the dough off the stamp and set onto the baking sheet.Use a round cookie cutter that's slightly smaller than the cookie stamp to cut the pressed cookie and trim off the uneven edges. Save the scraps.Repeat pressing all the cookies, dipping the stamp in flour and tapping off the excess in between each.

Step 6

Gather up all the scraps from the trimmed edges, roll into a ball, dust in flour, and press one more cookie, for a total of 13 cookies.Place all the pressed cookies about 1 inch apart on the baking sheet.

Step 7

Set the baking sheet in the refrigerator and chill the pressed cookies for 1 hour. Chilling the dough prior to baking ensures that the dough maintains its shape in the oven and doesn't spread.

Step 8

Preheat the oven to 350 F. Bake the chilled cookies on the center oven rack for 11 1/2 minutes.

Step 9

Cool the cookies on the pan for 5 minutes, then carefully transfer them to a cooling rack. Brush with the glaze while the cookies are still warm.

Step 10

As soon as you take the cookies out of the oven, prepare the glaze. In a bowl, whisk together all ingredients until smooth. The glaze should be fairly thin, about the consistency of warm honey.

Step 11

After cooling the cookies on the baking sheet for 5 minutes, transfer them to a cooling rack. They're ready to be iced right away.

Step 12

Dip a pastry brush into the icing, getting a generous amount onto the brush. Brush it over the cookies, getting it into all the crevices, and letting it drip over the sides. Repeat with all the cookies.

Step 13

Once you've iced a cookie, the glaze will crust and set quickly, so leave it alone. Don't brush over it again, and don't touch it. The glaze will set in about 30 minutes. Let the icing harden completely, about 2 hours, before storing the cookies in an airtight container.