Preheat the oven to 175 C and grease a 9 inch springform tin.
Melt the chocolate in a double boiler or microwave and set aside to cool slightly. Sift the flour and baking soda. Set aside.
In a large mixing bowl, beat the butter and sugar with a hand mixer on medium speed till light and creamy. Add the yoghurt and beat on low speed to combine.
Now add the eggs and vanilla extract and beat to combine. The mixture may appear curdled but it will stabilise in the next step.
Next, add the melted chocolate, and beat briefly on low speed until just combined. It will now be smooth and thick.
Finally add the flour mixture, spoon by spoon, alternating with the hot water. Mix in the water completely before adding the flour, to avoid lumps. Do this by hand because a mixer causes the batter to splatter too much and also beats too much air into the liquidy batter.
If you notice some lumps in the batter when all the flour is mixed in, run a hand mixer through it on low speed for a few seconds. The batter is slightly runny.
Pour the batter into the prepared loaf tin and bake for 50 minutes to an hour, till a toothpick poked in the center comes out clean. The cake will dome and crack a bit. Let the cake cool completely at room temperature. The cake can be left out overnight, loosely covered and in fact, I recommend it because the texture and flavour both improve. Before you frost it, chill the cake for 1 hour.
To make the frosting, beat the cream cheese and butter till smooth. Sift in the cocoa and sugar and beat again until creamy and slightly thickened. Refrigerate for 15 to 20 minutes. This is not a heavily frosted cake, I prefer it this way but you can definitely double the quantity if you like.
In the meantime, even out the top of the chilled cake by slicing off the domed portion. Slice the cake horizontally in two. Lift the top half off carefully and set aside. Spread half the frosting on the bottom half, then gently place the top half back on it, and frost the top as well. Spread the frosting to the sides and smoothen it out. Decorate the top with grated chocolate!
Refrigerate for 20 minutes before slicing and digging in! Store in the fridge for 5 to 6 days. Bring individual pieces to room temperature before eating. Happy baking!