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Heat oven to 180C/160C fan/gas 4. Grease a 20 x 30cm tin, then line with baking parchment. Beat the butter, flour, sugar, baking powder, eggs, yogurt, milk and vanilla until lump-free. Stir in the chopped chocolate. Spoon into tin; bake for 25-30 mins until golden and risen and a skewer comes out clean. Cool in the tin.
Melt the rest of the chocolate. Stir icing sugar into soft cheese, then the chocolate until smooth. Chill, spread over the cake, then cut into squares and decorate.