How to Make It
Preheat the oven to 350°. Line two 9-by-2-inch round cake pans with wax paper and grease the paper.
In a large bowl, sift together the cake flour, baking soda, baking powder and salt. In a medium saucepan, combine the brown sugar, granulated sugar, chocolate and 1/2 cup of water and cook over moderately low heat, stirring, until smooth. Let cool slightly, stirring occasionally.
Using an electric mixer, beat the butter and egg yolks until blended. Gradually beat in the chocolate mixture. Beat in the dry ingredients in two batches, alternating with the milk, until smooth. Beat in the vanilla. (The batter will be rather thin.)
In a medium bowl, using clean beaters, beat the egg whites until barely firm. Stir one-third of the whites into the batter. Fold in the remaining whites until incorporated.
Scrape the batter into the two prepared pans. Bake the cakes in the bottom third of the oven for 25 to 30 minutes, or until a cake tester inserted in the center comes out clean. Let the cakes cool for 15 minutes, then remove from pans and place right side up on racks to cool completely.
In a saucepan, melt half of the chopped chocolate in the heavy cream over moderately low heat, stirring. Remove from the heat and stir in the vanilla and remaining chopped chocolate until smooth. Scrape the ganache into a bowl and refrigerate until chilled, at least 3 hours or overnight.
Using an electric mixer, briefly beat the ganache until thick enough to hold its shape. Do not overbeat or the ganache will become grainy; if it does, melt it again over low heat and then beat it once more.
Peel off the paper from the cake layers. Place 1 layer right side up on a cake platter and spread 1 scant cup of the whipped ganache on top. Place the second cake layer upside down on top of the filling. Spread the sides and top of the cake evenly with the remaining whipped ganache. If desired, reserve about 1/2 cup of the ganache for decorating as follows: using a pastry bag fitted with a star tip, pipe simple stars or a scallop trim around the top or the base of the cake. Sprinkle the grated chocolate all over the top of the cake. To serve, slice gently with a serrated cake knife.
The cake can be refrigerated for up to 1 day.