Line baking sheet with parchment paper or silicone baking sheet mat.
In bowl of electric mixer, cream butter and sugars until fluffy, about 3 minutes. Add eggs one at a time, creaming well in between each egg addition. Add vanilla and blend.
In separate bowl, sift flour, espresso powder, cocoa, baking soda and kosher salt. Mix in half of flour mixture to sugar mixture and mix. Add remaining half and mix. Mix in chocolate chunks.
Drop cookies by rounded tablespoon onto baking sheets. Bake 12 minutes. Remove from oven and move to cooling rack to cool completely.
Once cookies have cooled completely, remove ice cream from freezer and let sit at room temperature for 3-5 minutes to soften slightly. Set ice cream container on its side. With sharp, serrated knife, cut through ice cream container into ½ to 3/4 inch rounds.
Working quickly, remove wrapper and place slice of ice cream on bottom side of cookie, then top with another cookie. Repeat with remaining cookies and serve immediately or wrap individually in plastic wrap, place in a freezer bag and freeze for later.