Preheat the oven to 200°C (approximately 390°F) In a large bowl, beat the butter, sugar and egg yolks together with a hand mixer until foamy. Stir in the ground almonds, ground walnuts, chopped almonds, rum, breadcrumbs, cocoa powder and grated chocolate. Beat the egg whites with a pinch of salt in a separate bowl until stiff peaks form. Gently fold the eggs whites into the nut mixture.
Grease a round, ovenproof dish. Pour in the cake batter and smooth top. Place the dish inside a larger dish and pour boiling water halfway up the cake dish. Bake for 45 minutes. Remove from oven and let stand for 10 minutes before serving.