How to Make It
Preheat the oven to 350°. Butter two 9-inch round cake pans and line the bottoms with parchment paper. Butter the parchment and dust with bread crumbs, tapping out any excess. In a food processor, pulse the walnuts until finely chopped. Add the cocoa powder, cake flour and espresso powder and pulse until the walnuts are finely ground. Transfer to a bowl.
In a large bowl, using an electric mixer, beat the yolks at medium speed until thick and pale, 3 minutes. Beat in 2/3 cup of the sugar; increase the speed to high and beat until thick, about 5 minutes. Beat in the vanilla. In a medium bowl, using clean beaters, beat the egg whites and salt at medium speed until soft peaks form. Gradually add the remaining 1/3 cup of sugar and beat at high speed until the whites are stiff and glossy. Fold the egg whites and ground walnuts into the yolk mixture in 3 batches; fold just until no streaks remain.
Divide the batter between the prepared pans; smooth the tops. Bake for about 20 minutes, until the cakes are golden and springy. Transfer to a rack for 10 minutes, then invert the cakes and cool completely. Peel off the parchment; turn the cakes right side up.
Fill a medium bowl with ice water. In a medium heatproof bowl, whisk the yolks, sugar and salt. Gradually whisk in the dissolved espresso. Place the bowl over a saucepan of barely simmering water and cook, stirring with a spatula, until the yolks are thick enough to coat the spatula and an instant-read thermometer inserted into the mixture registers 175°, about 10 minutes. Set the bowl in the ice bath and cool, stirring occasionally.
In a large bowl, using an electric mixer, beat the butter at medium speed until smooth. Beat in the yolk mixture in 4 batches, beating well between additions. Beat in the liqueur and vanilla.
Using a serrated knife, split each cake in half horizontally. Set a top layer, cut side up, on a cake plate; brush it with 2 tablespoons of the rum and spread with 1/2 cup of the filling. Top with a bottom cake layer; brush with 2 more tablespoons of rum and spread with another 1/2 cup of filling. Repeat with the remaining top cake layer, ending with the bottom layer, cut side down. Brush the top of the cake with the remaining 2 tablespoons of rum and spread the sides of the cake with a thin layer of filling. Spread the remaining filling on the top. Press the chopped walnuts around the side of the cake. Refrigerate the cake for at least 4 hours or overnight. Let the cake stand at room temperature for 15 minutes, then scatter the walnut halves on top before serving.