Special equipment: an 18-by-13-inch rimmed baking sheet
Preheat the oven to 350 degrees F. Line an 18-by-13-inch rimmed baking sheet with foil, leaving a 2-inch overhang on at least 2 sides. Butter the foil.
Whisk together the flour, cocoa powder and salt in a medium bowl. Melt the butter and chocolate in a medium saucepan over medium heat, stirring frequently, then remove from the heat and let cool slightly. Stir in the sugar and eggs, then add the flour mixture and stir to combine. Pour the batter into the prepared pan and bake until a toothpick inserted in the center comes out with just a few crumbs adhering, 20 to 25 minutes. Let cool completely in the pan on a cooling rack, then place in the freezer to firm up, about 30 minutes.
Use the foil overhang to help lift the brownie out of the pan and carefully flip it over onto a cutting board, making sure that it does not bend or crack. Peel the foil away from the bottom, then discard the foil and line the baking sheet with plastic wrap.
Using a warm knife, trim the rough edges off of the brownie so it is even (the brownie should be 16-by-12-inches). Cut the brownie in half crosswise, resulting in 2 pieces that are 12-by-8-inches. Lay one of the brownie pieces onto the prepared baking sheet, top-side facing down. Working quickly, use a large ice cream scoop to spread the ice cream evenly across the brownie, getting close to the edge. Use an offset or rubber spatula to help smooth out the sides and top of the ice cream. Place the other brownie piece on top and gently press to create one large ice cream sandwich. Fold the plastic wrap around the assembled ice cream sandwich to help hold its shape, then return it to the freezer to harden, at least 6 hours or up to overnight.
Use a warm knife to cut twenty-four 2-inch-square ice cream sandwiches. Roll the edges of each sandwich into the chopped espresso beans until they stick to all of the exposed ice cream edges. Wrap each sandwich in parchment paper and enjoy.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.) Before serving, let the ice cream sandwiches sit at room temperature for a few minutes so the brownies and ice cream can soften, making them easier to eat.
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