In a small saucepan set over low heat, combine the stout and butter, stirring frequently till melted. Turn off the heat, stir in the sugar and set aside to cool a bit.
In the meantime, sift the flour, baking soda and cocoa in a bowl. Set aside.
Grease a 9" round cake tin (preferably springform) and preheat the oven to 180 C.
In a large mixing bowl, lightly beat the eggs with the hand mixer, then add the yoghurt and vanilla and beat to combine well. The mixture might look a little curdled.
Now add the flour mixture gradually, alternating with the cooled beer mixture, beating on low speed as you go. (A stand mixer helps if you prefer to have both hands free in this step). Make sure there are no lumps in the batter and use the hand mixer to smoothen it out as needed.
Pour the batter into the prepared tin and bake for 50 minutes or until the cake has risen and domed and a toothpick poked into the center comes out clean. Start checking for doneness at around 40 minutes.
Allow the cake to cool completely at room temperature before frosting, especially if you plan to slice it in the middle and layer it with frosting.
To make the frosting, first add the chocolate to a heatproof bowl. Then combine the cream, stout and sugar in a small saucepan, set on low heat. Stir constantly to prevent the mixture from burning or splitting because of the alcohol. Heat until gently simmering then pour immediately over the chocolate. Let it sit undisturbed for a few minutes, then stir to combine and melt the chocolate. If there are a few lumps left, set the bowl over a pot of simmering water (don't let it touch the water) and gently warm the ganache, stirring till it's smooth.
Set this aside to cool and thicken for about 10 minutes. In the meantime, use a long, sharp knife to cut off any domed or uneven bits from the top of the cake. Then spread the frosting all over the surface of the cake and the sides, if you wish. Let the ganache set on the cake for another ten minutes, then for the best texture, slice and serve immediately!
Once frosted, the cake needs to be stored in the fridge where it will keep for about a week. Best served at room temperature or lightly warmed. It should also freeze well. While the flavour of the stout is subtle when freshly baked, I found that it intensifies after a few days but in a delicious way! Happy baking :)