Chill a metal mixing bowl and whisk or beaters in the freezer for 10 minutes. Line the base of an 8-inch springform pan with parchment; if you have acetate, line the sides and set the pan in the freezer.
Heat the oven to 340°F (171°C). Grease an 8-inch round cake pan, line the bottom with parchment, and dust the sides lightly with cocoa.
Bloom the cocoa: In a heatproof cup, whisk the hot milk, cocoa powder, and espresso powder until smooth and glossy. Let stand 5 minutes to cool slightly.
Make the batter (reverse-mix): In a large bowl whisk flour, baking powder, salt, and sugar. Add eggs, oil, vanilla, and sour cream; whisk until thick and mostly smooth. Stream in the warm cocoa-milk and whisk just until combined and no dry streaks remain.
Bake: Pour into the prepared pan and bake 24–27 minutes, until the center springs back and a toothpick shows a few moist crumbs. Cool 15 minutes, then turn out to a rack and cool completely.
Firm and split: Wrap the cooled cake and freeze 30 minutes to make slicing easy. Using a long serrated knife, split horizontally into two even layers.
Soften the ice cream at room temperature 10–15 minutes until spreadable but not melty. Place one cake layer into the chilled springform pan. Spread about 3/4 of the ice cream evenly over the cake, pressing to eliminate gaps. Top with the second cake layer and add the remaining ice cream if space allows, smoothing the top flush with the rim. Freeze until solid, at least 3–4 hours (overnight for the cleanest slices).
Whip the topping: In the chilled bowl, beat the cold cream to soft peaks. Sift in powdered sugar and cocoa, add vanilla and a pinch of salt, and whip to medium-stiff peaks that hold lines but still look silky.
Finish: Unmold the cake, remove acetate/parchment, and frost the top and sides with cocoa whipped cream. Create swirls with an offset spatula. Freeze 20–30 minutes to set before serving.
Serve: Warm a sharp knife under hot water, wipe dry, and slice. Return leftovers to the freezer well covered.