Preheat the oven to Gas mark 4/180°C/Fan 160°C. Heat the Guinness and butter in a saucepan until the butter melts. Then whisk in the cocoa powder and sugar, making sure there are no clumps of sugar and stir through the vegetable oil. Leave to cool.
Stir together the eggs, yogurt and vanilla. Tip the flour, baking soda and powder into a bowl. Pour in the Guinness mixture and stir together. Then gradually beat in the egg mixture until smooth.
Butter and line the base of a 23cm springform cake tin with nonstick baking paper. Pour in the cake mixture and bake for 45mins or until a metal skewer inserted into the centre of the cake comes out clean. Leave in the tin for 5mins, then turn out onto a wire rack and leave to cool completely.
To make the frosting, beat together the sugar and butter until very smooth. Then drain any water from the cream cheese and beat into the butter, a tablespoon at a time, until it is light and fluffy. Spread over the cooled cake with a palette knife and serve.