Position oven racks in the upper and lower thirds of the oven and heat the oven to 300ºF. Line two baking sheets with parchment.
Combine the butter, sugar, and salt in a stand mixer bowl (use the paddle attachment) or a large mixing bowl. Mix on low speed until the butter combines with the sugar but isn't perfectly smooth, 1 to 2 minutes. Add the flour and ground espresso and mix on low speed, scraping the bowl frequently, until the dough has just about pulled together, about 3 minutes; don't overmix.
On a lightly floured surface, roll the dough to about 1/4 inch thick. Aim for a uniform thickness to ensure even baking. Using a heart or other shape cookie cutter, cut out shapes as close to one another as possible. Press the scraps together, roll them out, and cut out more cookies. If the dough becomes sticky, refrigerate it briefly. Arrange the cookies on two parchment-lined baking sheets and refrigerate until chilled, at least 20 minutes.
Bake the cookies until golden on the bottom and edges and pale to golden on top, 30 minutes to 1 hour. (After 15 minutes, swap the position of the baking sheets and rotate them 180 degrees for even baking.) If the cookies are done before 30 minutes, reduce the oven temperature to 275° F for the remaining batches; if they take longer than 1 hour, increase the temperature to 325° F.
Dip the baked, cooled cookies
Set a sheet of parchment or waxed paper on a work surface. Put the chocolate and shortening in a small heatproof bowl and set the bowl over a pan of simmering water. Melt the chocolate, stirring, until it's smooth and warm; don't let it get hot. Dip half of each cookie into the chocolate. Set the cookies on the parchment and let the chocolate set up at room temperature, about 2 hours.
Photo: Anna Williams