Preheat the oven to 325°F. Grease bottom/sides of two square 9-inch metal baking pans and line bottom with parchment, and lightly grease the parchment. Set aside
Whisk together the flour, baking powder, baking soda and salt in a bowl.
Melt the butter in the microwave, then add the cocoa powder and whisk it in to make a thick paste. Add the sugars to the paste, along with the warm coffee, and the buttermilk, egg, and vanilla. Then whisk in the flour.
Divide the batter between the prepared pans, smoothing the tops with an offset spatula, and then bake them for about 20 minutes or until a cake tester inserted into the center comes out clean, except for a couple crumbs.
Cool slightly then unmold onto a parchment lined cooling rack to cool completely.
Wrap the layers in plastic wrap and freeze them for about an hour.
Line on of the square metal baking pans with lots of plastic wrap. Soften the ice cream for about 10–20 minutes (alternately if it’s homemade ice cream do this step directly when it’s done churning!), then fill the lined baking pan with the ice cream, smoothing it into an even layer with a small offset spatula. Fold over the plastic overhangs to cover and seal the ice cream, then freeze it for about an hour.
When all the components are frozen, unwrap everything, and then flip one of the cake layers so that it is top side down, top with the square ice cream layer, lining up the corners, then top with the second cake layer, top side up. Wrap the whole thing in plastic wrap and freeze again.
Unwrap the giant ice cream sandwich and cut into 16 squares (I used a serrated knife for this) and serve immediately or wrap each quickly in parchment and store in a container in the freezer.