Line a 9x13-inch baking dish with foil, allowing excess to hang over the edges.
If you're using homemade ice cream, immediately after churning, spread the ice cream into the prepared pan. If using store-bought ice cream, soften it slightly and then spread it into the prepared pan. Freeze overnight.
Preheat oven to 350 degrees F.
In a large mixing bowl, beat together the shortening and the brown sugar with an electric mixer for 2 to 3 minutes. Add the baking powder, salt, cocoa powder, espresso powder and vanilla. Mix until incorporated. Mix in 1 cup of the flour, followed by 2 tablespoons of water, and then add the remaining 1 cup flour and another 2 tablespoons of water, mixing well until no dry ingredients remain (give it some time, up to 5 minutes of mixing). The dough should be soft and pliable but not sticky; if necessary, add more water, a teaspoon at a time, until the dough comes together.
Turn out half the dough onto a lightly floured surface and roll to an even 1/8-inch to ¼-inch thickness. Cut the dough into 2x4-inch rectangles (you could also cut into squares, or use a cookie cutter to make circles).
Transfer the cookies to a baking sheet lined with parchment paper. Using a skewer (or the tip of a thermometer - works awesome!), poke a pattern of holes on each cookie's surface. Roll out, cut, and poke remaining dough, rerolling the scraps as you work. Place the sheets of cookies in the freezer for 10 minutes before baking.
Bake 7 to 8 minutes, or until the cookies are just set. Do not overbake.
Remove from the oven and let the cookies cool 2 to 3 minutes on a baking sheet. Transfer to cooling racks and cool to room temperature. Freeze cookies for at least 1 hour before assembling the sandwiches.
To assemble the sandwiches, have everything ready and work quickly! Match up cookies of the same size and have them laid out and ready for the ice cream. Use the edges of the foil to lift the block of firm ice cream from the baking pan and place it on a cutting board. Working quickly, cut the ice cream into 2x4-inch rectangles (you'll have a little ice cream left over). Using a narrow stainless steel spatula, place a rectangle between two chilled cookies and press the cookies lightly to adhere. (I found it easiest to do this one at a time. Cut one or two rectangles, assemble those cookies and place on a tray, then do one or two more, etc. until you're finished.) Return the sandwiches to the freezer for at least 30 minutes. Wrap individually in plastic wrap and store in an airtight container or zip-top plastic bag in the freezer.