Preheat the oven to 180°C (Electric oven | Electric fan oven 160°C | Gas Mark 4) and place the paper cases into a muffin tin.
Melt the butter in a saucepan over a gentle heat. Add the chocolate and continue stirring until smooth.
Allow to cool slightly and then put into a bowl and beat in the eggs and sugar, and then stir in the flour, bicarbonate of soda, cocoa powder and chopped walnuts. Combine to a smooth mixture.
Drop the chocolate brownie cupcake mixture into the paper cases and bake in the oven for about 25 minutes. Allow to cool a little and then lift the chocolate brownie cupcakes out of the muffin tin and leave to cool on a wire rack.