Preheat oven to 350ºF. In a large bowl, whisk together flour, cocoa powder, baking powder, baking soda, and salt. Set aside.
Beat butter and sugar in a standing mixer until light and fluffy, about 2 minutes, pausing occasionally to scrape down sides and bottom of bowl with a rubber spatula. Beat in egg, then vanilla extract.
With mixer speed on low, beat in ? of the flour mixture, followed by ½ of the buttermilk. Repeat, ending with the final ? of the flour mixture.
Drop by level tablespoonfuls onto parchment-lined baking sheets. Bake 5-6 minutes, or until they just lose most of their sheen but are still slightly underdone - if you press the centre, it will leave an indent. (Slightly undercooking them is essential to chewy, delicious cookies.) Cool completely on wire racks, then freeze in a single layer until very firm.
Soften the ice cream at room temperature for about 10 minutes. Spread one cookie with 2 tablespoons of ice cream then top with a second cookie. Transfer to a parchment-lined baking sheet. Repeat with remaining cookies, then freeze on the baking sheet in a single layer until firm. Transfer to a large freezer bag. Before serving, let stand at room temperature for a few minutes to re-soften ice cream.