Prepare the pan: Line a loaf pan or springform with plastic wrap or parchment, leaving overhang for lifting.
This keeps the cake neat and easy to slice.
Make the coffee soak: Combine the cooled espresso with the coffee liqueur. Set aside in a shallow dish for quick dips.
Whip the cream: In a cold bowl, whip the heavy cream with the powdered sugar and vanilla to soft peaks. Do not overbeat.
Blend the mascarpone: In another bowl, stir mascarpone with a pinch of salt until smooth.
Gently fold in the whipped cream to create a light, silky mixture.
Soften the ice cream: Let the coffee ice cream sit out for 5–10 minutes until spreadable but not runny. If it gets too soft, pop it back into the freezer for a few minutes.
Build the first layer: Quickly dip half the ladyfingers or cookies into the coffee mixture (1–2 seconds each). Arrange in a snug layer in the pan.
Spread the ice cream: Add half the coffee ice cream over the cookies.
Smooth the top. Sprinkle with half the chopped chocolate.
Add the mascarpone layer: Spread half the mascarpone-cream mixture over the ice cream. Dust lightly with cocoa.
Repeat: Make a second dipped-cookie layer, then the rest of the ice cream, remaining chocolate, and the final mascarpone layer on top.
Finish and freeze: Generously dust the top with cocoa.
Cover and freeze for at least 6 hours, preferably overnight, until firm.
Unmold and serve: Lift out using the overhang. Let sit at room temperature for 10 minutes to soften slightly. Slice with a warm, dry knife for clean cuts.