For the cake: Preheat your oven to 350 degrees F. Grease an 8-inch or 9-inch round cake pan, or an 8-inch square pan. I also like to line the bottom of the pan with parchment paper, to give extra insurance that the cake will come out cleanly. Just trace the bottom of the pan on a sheet of parchment paper and cut it out, then place inside the pan.
In a large bowl, whisk together dry ingredients: flour, cocoa powder, sugar, salt, espresso powder, and baking soda. Make sure to whisk vigorously and tamp out any cocoa powder lumps.
Pour in the wet ingredients: coffee, olive oil, vanilla, vinegar. Whisk it all together until a smooth batter is formed. You’ll notice it might get a little foamy – that’s the baking soda/vinegar reaction happening. Stop whisking when the mixture is combined and no lumps remain – don’t overmix or the cake will be tough.
Pour batter into prepared pan, and bake for 28-32 minutes if using a 9-inch round pan, or 32-34 minutes if using an 8-inch round or square pan, until cake springs back when touched and a tester inserted in the center comes out clean.
Let cake cool in pan on a rack for 10 minutes, then invert the pan onto the rack to release the cake, remove the parchment from the bottom, and flip back right side up onto a cake plate. Let cake cool while you prepare the ganache.
Lightly butter a 9-inch springform pan. Spread the chocolate ice cream into an even layer in the bottom of the springform pan. Place in the freezer for 30 minutes. Spread the hot fudge sauce over the chocolate ice cream (if it had been chilled, you’ll need to rewarm briefly), then sprinkle the chopped Oreo cookies, pressing lightly so that they adhere to the hot fudge. Return to the freezer for at least 30 minutes. Lastly, dollop the vanilla ice cream over the chopped Oreos and gently spread into an even layer. Freeze for at least 8 hours, or overnight.
At least 1 hour (and no more than 12 hours) before serving, unmold the cake. To release the cake from the pan, invert the cake onto a plate or cardboard round the same size and wrap a hot kitchen towel around the cake pan, keeping it there for 30 seconds, or until the cake loosens, and slide the pan off. Remove the bottom of pan. Top with a serving plate and turn the cake right side up. Return to the freezer for at least 10 minutes.
While the cake is in the freezer, make the whipped cream. Combine the heavy cream, sugar and vanilla extract in the bowl of a stand mixer. Using the whisk attachment, whip on medium-high speed until the cream is light and fluffy and holds a medium to firm peak, 2 to 3 minutes.
Spread the whipped cream on the cake, working quickly so that the ice cream doesn’t melt. (If it gets soft, just pop it back into the freezer for 5 minutes.) I used a Wilton #21 decorating tip to pipe a shell border around the top and bottom of the cake. Decorate with sprinkles on top, if desired.
Remove the cake from the freezer 5 minutes before serving to soften it slightly. A hot, dry knife will yield the cleanest cuts. Dip your knife in a glass of hot water, wipe it clean with a towel, and cut a slice. Repeat between every slice.