"This is a famous Italian chocolate cake originally from Capri but popular throughout Southern Italy, where every family has its own recipe. It's a rich, dense chocolate cake that's made either with ground almonds or walnuts. Walnuts are used here, but you can substitute them with the same weight of ground almonds, if desired. Dust with confectioners' sugar before serving."
Preheat oven to 375 degrees F (190 degrees C). Grease and flour a 9-inch round cake pan.
Beat egg whites in a glass, metal, or ceramic bowl until stiff peaks form.
Beat egg yolks lightly in a separate bowl.
Heat chocolate in top of a double boiler over simmering water, stirring frequently and scraping down the sides, until melted, about 5 minutes. Remove from heat.
Combine 1/2 cup plus 2 tablespoons sugar and 1/2 cup plus 1 tablespoon butter in a large bowl; beat with an electric mixer until creamy. Stir in egg yolks, melted chocolate, walnuts, flour, and baking powder until smooth. Fold egg whites gently into the batter.
Pour batter into the prepared cake pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Let cool completely before serving.