Preheat the oven to 180°C (350°F). Grease and line one 7-inch round cake pan.

Whisk 3 eggs and 100 g caster sugar for 5 to 7 minutes. Continue until the mixture triples in volume and falls in thick ribbons.

Add 1 teaspoon vanilla extract to the egg mixture. Whisk briefly just until incorporated.

Sift 100 g all-purpose flour over the whipped egg mixture. Fold gently with a rubber spatula until no dry flour remains.

Fold 15 g melted unsalted butter into the batter. Stop mixing as soon as the batter is uniform to preserve its airiness.

Pour the batter into the prepared 7-inch round cake pan. Bake for 20 minutes at 180°C (350°F).

Test the sponge with a cake skewer; it should come out clean. Cool the cake in the pan briefly, then cool completely on a cooling rack.

Whip 1 cup heavy whipping cream, 1/2 cup mascarpone cheese, and 3 tablespoons icing sugar until thick and spreadable. Keep the mascarpone whipped cream chilled.

Slice the cooled sponge horizontally into 2 layers. Brush both cut sides generously with 1/2 cup cold brew coffee.

Place one soaked sponge layer on a serving plate and spread on half the mascarpone whipped cream. Top with the second soaked sponge layer.

Cover the top of the cake with the remaining mascarpone whipped cream. Dust the surface lightly with cocoa powder.

Chill the assembled cake until fully set, about 60 minutes. Slice the chilled cake into 8 portions before serving.