Preheat oven to 180°C and grease a 24cm loose-bottomed tin with butter and baking paper.
Melt chocolate and butter in a heatproof bowl over simmering water then set aside to cool.
Arrange fig halves cut-side down in circles on the bottom of the prepared tin.
Whisk egg yolks with sugar until pale and thick, then stir in the orange liqueur.
Whisk egg whites in a separate bowl until soft peaks form.
Combine the egg yolk mixture with melted chocolate and gently fold in the egg whites.
Pour the mixture over the figs and bake for 18 to 20 minutes until just set.
Whip the double cream to soft peaks and stir in orange liqueur to taste.
Dust the finished cake with cocoa powder and serve with the prepared boozy cream.