Preheat the oven to 350 degrees F/180 degrees C. Grease an 8-inch/20-cm round cake pan and line with parchment paper.
Grind the walnuts together with the breadcrumbs in a food processor. Put the egg whites in a large bowl for whisking. Whisk the yolks and granulated sugar in a bowl set over a saucepan of simmering water (without letting the bowl touch the water) until they have tripled in volume and become thick, pale and ribbony. Take the yolk mixture off the heat. Scatter the nut mixture over the yolk mixture, along with the chocolate, if using, then drizzle over the butter and espresso. Fold very gently to blend. Whisk the egg whites to stiff peaks. Stir a spoonful of whites into the batter to loosen it, and then gently fold in the remainder.
Pour the batter into the prepared cake pan. Bake until a toothpick inserted into the center comes out clean, 35 to 40 minutes. Remove from the oven and let cool on a wire rack before flipping the cake out onto a serving plate.
Decorate with a sifting of confectioners' sugar and a few walnut halves. Some white blossoms look nice, too. Serve small portions of cake with whipped cream and chocolate shavings or with coffee ice cream.