Mix the 3 whole eggs with the sugar in a non-boiling double boiler. While still warm, remove from the heat and whip until doubled in volume. Add the sifted flour. Pour into the buttered cake pan after having covered the bottom with buttered wax paper. Put in an open oven (350F) for 15 minutes, then close the oven. When the dough resists the pressure of your finger, check the baking. Turn out on a cake rack. Leave to cool.
The butter custard: moisten the sugar, cook until you obtain a thick syrup. Beat the egg white until stiff, pour in the boiling sugar syrup little by little, whip until almost cold. Add the chocolate, melted in a double boiler, then the very softened butter. Assembly: cut the Genoese into two round slices. Moisten the first slice with the rum syrup, then spread with 2/3 of the butter custard. Moisten the second slice, lay over the first. Cover the cake completely with the remaining custard. Chill for 2 hours. The mousse: make the same syrup as the one used for the butter custard. Beat the white until stiff, pour in the syrup, whipping continuously, add the chocolate. Use to cover the cake in a dome shape. Top with the chopped chocolate. Sprinkle with confectioner╒s sugar. Serve cool or cold.