Preheat oven to 350°F (175°C). Line a 10x15-inch jelly roll pan with parchment paper and lightly grease.
Whip the eggs and 1/2 cup sugar for 5 minutes until pale and tripled in volume.
Sift the flour, cocoa powder, remaining sugar, baking powder, and salt. Gently fold into the egg mixture. Fold in the vegetable oil.
Spread the batter evenly in the pan and bake for 10-12 minutes.
Immediately turn the hot cake out onto a cocoa-dusted kitchen towel. Peel off the parchment and roll the cake up inside the towel. Let cool completely.
Fold the crushed Oreos into the softened ice cream.
Carefully unroll the cooled cake, spread the ice cream mixture evenly leaving a 1-inch border, and re-roll the cake without the towel.
Wrap tightly in plastic wrap and freeze for at least 4 hours.
Heat heavy cream and pour over dark chocolate chips. Whisk until smooth to create the ganache. Drizzle over frozen cake before slicing.
