Preheat your oven to 350°F (175°C). In a double boiler, melt the bittersweet chocolate and butter together, stirring until smooth. Remove from heat and stir in the espresso powder and vanilla extract. Allow to cool slightly.
In a mixing bowl, whisk together the eggs, brown sugar, and salt until thick and pale. Gradually fold in the melted chocolate mixture.
In a separate bowl, mix the cocoa powder with hot water until smooth. Gently fold this into the chocolate-egg mixture until well combined.
Pour the batter into a prepared cake pan and bake for 25-30 minutes, or until a toothpick comes out clean. Allow to cool completely in the pan.
Melt the semi-sweet chocolate using the double boiler method. In a mixing bowl, whip the cold heavy whipping cream until soft peaks form. In another bowl, combine granulated sugar, salt, and melted chocolate. Fold in the whipped cream until blended.
Once the cake has cooled, spread the semi-sweet chocolate mousse evenly over the top. Chill in the refrigerator while preparing the white chocolate mousse.
Melt the white chocolate in the double boiler. Sprinkle gelatin over water and let it bloom, then add it to the melted white chocolate and stir until dissolved.
Whip the remaining heavy whipping cream until soft peaks form. Gently fold in the melted white chocolate mixture until fully combined.
Pour the white chocolate mousse over the semi-sweet chocolate mousse layer. Smooth the top and refrigerate for at least 4 hours or overnight for best results.