Melt the dark chocolate and butter in a double boiler, then let it cool slightly.
In a bowl, whisk the eggs with the granulated sugar until light and fluffy.
Add the melted chocolate and butter mixture to the egg mixture, then stir until smooth.
Sift together the flour and cocoa powder, and stir in the vanilla extract. Gently fold the dry ingredients into the chocolate mixture until just combined.
Pour the batter into a greased cake pan and bake in a preheated oven at 350°F (180°C) for 25-30 minutes. The center should remain slightly fudgy.
While the cake is cooling, whip the heavy cream with the powdered sugar until stiff peaks form.
Once the cake has cooled completely, spread the whipped cream over the top and sprinkle with chocolate shavings.
Refrigerate the cake for at least 2 hours to allow the flavors to meld and the cream to set.
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