Preheat oven to 375°F.
Line jelly roll pan with parchment paper.
Beat eggs and sugar until thick and pale.
Fold flour and cocoa powder gently into mixture.
Add vanilla extract and mix briefly.
Spread batter evenly in prepared pan.
Bake for 12-15 minutes until springy.
Turn cake onto clean towel dusted with cocoa.
Roll cake tightly in towel while warm.
Cool completely on wire rack.
Beat mascarpone, cream, and powdered sugar until smooth.
Combine espresso and coffee liqueur in small bowl.
Unroll cooled cake carefully.
Brush cake with espresso mixture evenly.
Spread mascarpone filling over entire surface.
Roll cake tightly without towel.
Wrap in plastic wrap and refrigerate 4 hours.
Dust with cocoa powder before serving.