Preheat oven to 350 degrees, setting rack at middle level. Butter a 10-inch round cake pan, 2 inches deep, and cut a piece of parchment or waxed paper to fit the bottom.
Cut the chocolate finely and place in a small bowl over hot water to melt, stirring occasionally. Remove the bowl from the pan and cool slightly.
In a large mixer, beat the butter with half the sugar until soft and light. Beat in the chocolate, then the yolks, one at a time, scraping bowl and beaters often. Continue beating until the mixture is smooth and light. Place the walnuts in the bowl of a food processor and grind them finely, pulsing the machine on and off at one second intervals. Be careful that the walnuts do not become pasty. Stir the walnuts into the batter.
In a clean dry bowl, beat the egg whites until they hold a very soft peak and beat in the remaining sugar in a slow stream. Beat the whites until they hold a soft glossy peak. Stir 1/4 of the whites
into the batter, then fold in the rest with a rubber spatula, so that no streaks remain.
Pour the batter into the prepared pan and smooth the top. Bake the Torta Caprese about 40 minutes, until the center is firm when pressed with a fingertip.
Cool the cake in the pan for 10 minutes. The cake may sink slightly, though this does not affect its texture. Trim off any loose crust and invert the cake on a rack, remove the pan and allow to cool completely. Dust cake with confectioners' sugar and slide onto a platter.