Dissolve the espresso in the boiling water, and set aside to cool.
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and confectioners’ sugar together on medium speed for about 3 minutes, until the mixture is very smooth. Beat in the vanilla and espresso.
Reduce speed to low and add the flour, mixing only until it disappears into the dough. Don’t work the dough much once the flour is incorporated.
Fold in the chocolate chips with a sturdy rubber spatula.
Using the spatula, transfer the soft, sticky dough to a gallon-size zipper-lock plastic bag. Put the bag on a flat surface, leaving the top open and roll the dough into a 9 x 10 inch rectangle that’s 1/4 inch thick. As you roll, turn the bag occasionally and lift the plastic from the dough so it doesn't cause creases. When you get the right size and thickness, seal the bag, pressing out as much air as possible, and refrigerate the dough for at least 2 hours, or for up to 2 days.
Preheat the oven to 325 degrees F. Line two baking sheets with parchment or silicone mats.
Put the plastic bag on a cutting board and slit it open. Turn the firm dough out onto the board (discard the bag) and using a ruler as a guide and a sharp knife, cut the dough into 1 and 1/2-inch squares. Transfer the squares to the baking sheets and carefully dock each one twice with a fork, gently pushing the tines into the dough. Be sure not to go through the dough, as it will likely cause the cookie to crumble (this is what happened to a few of mine).
Bake for 18 to 20 minutes. The shortbread will be very pale. They shouldn't take on much color.
Transfer the cookies rack to cool completely.