Make the chocolate cookies: Preheat the oven to 350 degrees F.
In a large bowl, combine the flour, cocoa powder, and salt. Whisk for 30 seconds to combine.
In the bowl of a stand mixer fitted with the paddle attachment, mix the butter and sugar until light and fluffy. Add the whole egg and mix to combine. Scrape down the bottom and sides of the bowl. Add the egg yolk and vanilla and mix to combine. With the mixer running on low speed, add the flour mixture and mix until just combined.
Divide the dough in half, shape each half into a disk, and wrap each piece in plastic wrap. Refrigerate the dough for 20 minutes.
Roll out each piece of the dough on a piece of parchment paper to a 9-by-12 inch rectangle. Transfer the two parchments with dough onto two sheet pans. Using a fork, dock the dough. Bake until just cooked through (make sure not to let the edges get crisp), 10 to 15 minutes. Let cool completely.
Assemble the sandwiches: Take the ice cream from the freezer and let sit at room temperature until just soft enough to spread, 5 to 10 minutes. Transfer the ice cream to a piping bag fitted with a large open round tip and pipe even lines to cover entire underside of one cookie. Alternatively, spread the ice-cream using an offset spatula.
Carefully top the ice cream with the second chocolate cookie rectangle. Wrap the sandwich with plastic wrap and freeze until just set, about 1 hour.
Run a sharp knife under hot water and dry completely. Using the hot knife, cut the large ice cream sandwich into 12 individual sandwiches. Put sprinkles, chopped pistachios, and chocolate chips in separate plates. Coat the edges of the sandwiches in the garnish of your choosing. Serve immediately or freeze until ready to eat.
Adapted from "Let Them Eat Cake" by Gesine Bullock-Prado © Stewart, Tabori & Chang 2015. Provided courtesy of Gesine Bullock-Prado. All rights reserved.