Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment. Scoop the ice cream in a large bowl and set aside at room temperature to slightly soften.
Beat the butter, confectioners' sugar and brown sugar in the bowl of a stand mixer fitted with the paddle attachment until pale and fluffy.
Sift together the 2 cups flour and the cocoa powder in a medium bowl. Add the salt and whisk to combine. Add to the creamed butter with the machine running on low speed.
Add the vanilla and chocolate and mix on low speed until the dough becomes a rich, dark brown.
Roll out the dough between 2 pieces of parchment to 1/4 inch thick. Using a 4-inch round cookie cutter, cut out 24 rounds. Reroll the scraps to stamp out more rounds.
Transfer the rounds to the prepared baking sheets and sprinkle with sanding sugar. Bake until they look matte, about 15 minutes, rotating the sheets halfway through baking. Let cool completely on wire racks.
Beat the ice cream with a handheld mixer until evenly soft. Scoop about 1/2 cup of the ice cream onto each bottom cookie. Close the sandwiches with the top cookies.
Place the coatings on separate plates. Roll the sides of each ice cream sandwich in your desired coating. I like to roll the vanilla ice cream sandwiches in sprinkles or grated chocolate, and the chocolate ones in chopped salted pistachios or cayenne.
Serve right away or wrap tightly in plastic wrap and freeze for up to 3 months.