Preheat the oven to 350°. Butter two 15-by-12-inch jelly roll pans and line the bottoms with parchment paper. In a medium saucepan, melt 6 ounces of the chopped chocolate with the butter and vanilla over very low heat, stirring gently. Remove the chocolate mixture from the heat and let cool slightly.
In a small saucepan, combine the cocoa with the water and bring to a boil, whisking constantly. Let cool slightly, then whisk the mixture into the melted chocolate. Whisk in the crème fraîche.
In a large bowl, using an electric mixer, beat the whole eggs, egg yolks and both sugars at medium speed until pale and fluffy, about 5 minutes. Beat in the chocolate mixture. In a medium bowl, whisk the flour with the baking soda, baking powder and salt and transfer to a sifter or a sieve. Sift the dry ingredients and fold into the cake batter with a large spatula until fully incorporated.
Spread the batter evenly between the prepared pans and sprinkle with the remaining 4 ounces of chopped chocolate. Bake the cakes in the lower and middle third of the oven for 25 to 30 minutes, until the centers spring back when lightly pressed; shift the pans halfway through baking. Let the cakes cool completely in the pans.
In a medium bowl set over a medium saucepan of simmering water, melt the white chocolate. Remove from the heat. Pour off the water in the saucepan and wipe it out. Add the heavy cream and butter to the saucepan and heat until the butter is melted and small bubbles appear around the edges. Whisk the hot cream mixture into the white chocolate. Set the bowl in a cool place until the ganache is firm enough to hold its shape, at least 1 hour.
In a medium saucepan, heat the cream until small bubbles appear around the edges. Put the chopped chocolate in a heatproof bowl and pour the hot cream on top. Let stand for 2 to 3 minutes, until the chocolate has melted, then whisk until smooth. Set the bowl in a cool place until the ganache is firm enough to hold its shape, at least 1 hour.
In a medium saucepan, melt the chocolate over very low heat, stirring frequently. In a small saucepan, whisk together the granulated sugar, corn syrup, cocoa and water and bring to a boil, whisking constantly. Remove from the heat and whisk in the brandy and melted chocolate. Let cool completely, about 30 minutes.
In the bowl of a standing electric mixer fitted with a wire whisk, beat the butter at medium speed until light and fluffy. Add the cooled chocolate mixture. At low speed, beat in the confectioners' sugar.
Cut out a 5-by-11-inch cardboard rectangle. Place a sheet of parchment or wax paper over each cake and top with a flat cookie sheet or cutting board. Invert the cakes and remove the pans. Keeping the paper attached, trim each cake to an even 15-by-11-inch rectangle, then cut each cake into three 5-by-11-inch rectangles; you will have 6 rectangles.
Spoon a small dollop of the chocolate frosting onto the cardboard rectangle and transfer one cake rectangle to it; peel off the paper. This will be the base. Spread half of the white chocolate ganache on the base and top with another cake rectangle; peel off the paper. Spread half of the dark chocolate ganache on the cake and top with another cake layer, peeling off the parchment. Spread with 1 1/4 cups of the chocolate frosting. Repeat with 2 more layers, peeling the parchment off the cake rectangles and spreading them with the remaining white chocolate ganache and dark chocolate ganache. Keep the sides even as you build the cake by smoothing them out with a metal cake spatula. Top with the final cake rectangle and peel off the parchment. Coat the sides and top of the cake with a smooth layer of chocolate frosting; refrigerate briefly to set the frosting. Spread the remaining frosting over the cake and garnish with the chocolate shavings. Carefully transfer the cake (on its cardboard base) to a platter and refrigerate until firm. Using a hot knife, cut the cake into slices while cold and let come to room temperature before serving.
Make Ahead
The cake can be refrigerated for 3 days or frozen for up to 2 weeks.
