Preheat the oven to 325 degrees F (165 degrees C). Lightly grease a springform pan with butter.
Place dark chocolate and butter in top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until chocolate is melted, about 5 minutes. Remove from heat. Stir in coffee and let cool slightly, about 5 minutes. Whisk egg yolks into the chocolate.
Whisk egg whites, brown sugar, and salt in a separate bowl until peaks are the consistency of firm snow. Fold into the chocolate mixture. Pour into the pan and smooth the top.
Bake in the preheated oven until firm, about 20 minutes. Cool for 1 hour.
Prepare the second layer while the first layer is cooling. Mix water and cocoa powder together in a bowl. Melt dark chocolate in top of a double boiler over simmering water, about 5 minutes. Remove from heat.
Whisk cream, mascarpone cheese, sugar, and salt together in a bowl. Add cocoa powder mixture and melted chocolate. Pour over the first layer. Refrigerate until set, at least 30 minutes.
Meanwhile, prepare the top layer. Melt white chocolate in top of a double boiler over simmering water, about 5 minutes. Remove from heat.
Dissolve gelatin powder in water; let stand for 5 minutes. Heat in a double boiler until melted, 2 to 3 minutes. Mix into the melted chocolate.
Whisk cream until soft peaks form. Add mascarpone cheese and mix until smooth. Fold in the chocolate-gelatin mixture. Pour over the second layer. Refrigerate cake until firm, at least 3 hours.
