In the large bowl of an electric mixer fitted with a paddle or beaters, on medium speed soften the butter. Add the brown and granulated sugars. When the sugar is incorporated, raise the speed to high and continue to beat until fluffy, scraping down the sides of the bowl and under the beaters with a rubber spatula, as necessary. Lower the speed to medium and add the eggs, 1 at a time, and the vanilla, again scraping down the sides of the bowl as necessary. Turn the speed to low, gradually pour in the flour mixture, and beat until just combined. Add the chocolate and nuts and again beat until just combined.
Sift together the flour, cocoa, espresso, baking soda, and salt. Set aside.
Scrape the dough out of the bowl and wrap in plastic wrap. Refrigerate 2 to 3 hours, up to overnight. Position the rack in the center of the oven and preheat the oven to 350 degrees F. Line 1 or 2 baking trays with parchment paper.
Remove the dough from the refrigerator and divide into mounds, about 1-ounce each (the size of an unshelled walnut). Roll between the palms of your hands, forming 60 to 62 balls of dough. Arrange the balls on the prepared trays, about 2 inches apart. Bake until slightly firm to the touch, 13 to 15 minutes, reversing the trays from front to back after 7 minutes to ensure even baking. Place the trays on racks to cool. After a few minutes, transfer the cookies to the racks with a wide metal spatula to continue to cool. If reusing the baking tray, cool slightly before arranging the balls of dough on it.
Take the ice cream out of the freezer and let soften slightly for 10 minutes. When the cookies have cooled, spread half of the cookies with some ice cream. Top with another cookie and press lightly. Wrap in plastic wrap and freeze until firm.