This elegant cake is perfect for the most important occasion and makes a spectacular dinner-party dessert. And it can be entirely made, except for the cocoa powder finish on top of the cake, the day before.

One 9-inch cake, about 12 servings

Cake Batter

1/4 cup water

6 ounces bittersweet chocolate, cut into 1/4-inch pieces

6 large eggs, separated directly into 2 mixer bowls

1/2 cup sugar

2 teaspoons vanilla extract

Pinch of salt

1/3 cup blanched (skinless) hazelnuts, lightly toasted and chopped but not ground

Milk Chocolate Mousse

4 large egg yolks

1/4 cup sugar

1/4 cup dark rum

12 ounces milk chocolate, melted and cooled

1/2 cup heavy whipping cream, whipped to a soft peak

Finely chopped toasted hazelnuts for the side of the cake; Dutch process cocoa for the top

3 nine-inch round layer pans buttered and the bottoms lined with buttered parchment

Set a rack in the middle level of the oven and preheat to 350 degrees.
For the layers, combine the chocolate and water in a large mixing bowl and set over a pan of gently boiling water, stirring occasionally until melted. Cool. Whisk the yolks by hand in the bowl of an electric mixer and whisk in half the sugar and the vanilla. Place on mixer with whisk and whip of medium-high speed until lightened, about 3 minutes. Scrape the yolk mixture over the melted chocolate but don’t fold it in.
Combine the egg whites and salt in a mixer bowl and whip on medium speed until white, opaque, and beginning to hold their shape. Increase the speed to medium-high and whip in the remaining 1/4 cup sugar a tablespoon at a time, until the egg whites hold a firm peak. Scrape a quarter of the whites over the yolk and chocolate mixtures in the bowl and stir together. Fold in the remaining egg whites.
Divide the batter evenly among the prepared pans and use a small offset spatula to spread it evenly. Scatter a third of the chopped hazelnuts on each layer.
Bake the layers until risen, fallen, and firm, about 12 to 15 minutes. As soon as you take them out of the oven, invert a layer to a cardboard, and lift off the pan, leaving the paper on the bottom. Replace the pan with another cardboard and invert again. Remove the top cardboard and let the layer cool on the bottom cardboard. Repeat with the remaining layers. Wrap the layers in plastic once they have cooled.
Before starting the filling, have the layers and a medium offset spatula and a cardboard to assemble the cake on ready nearby. For the filling, whisk the egg yolks by hand in a medium mixing bowl. Whisk in the sugar and the rum. Place the bowl over a pan of gently boiling water and whisk until thickened, about 3 minutes. Remove the bowl from the pan and continue whisk until cooled to room temperature. Scrape the yolk mixture over the melted chocolate but don’t mix it in; quickly fold in the cream until the filling is smooth and can hold its shape.
Invert one of the layers (nut side down) to a cardboard, peel off the paper, and spread with a third of the filling. Repeat with a second layer and another third of the filling.
Invert the last layer to the filling and peel off the paper. Cover the entire outside of the cake with a thin coat of the remaining filling. Press the chopped hazelnuts against the side of the cake.
Dust the top of the cake with cocoa and use a serrated knife to trace a lattice pattern into it.
Keep at a cool room temperature until ready to serve. For advance preparation, don’t finish the top of the cake, wrap in plastic and chill. To serve, unwrap, bring to room temperature, and finish as in step 9.