Line a square 20x20cm/8x8" baking tin with greaseproof paper leaving a slight overhang to allow you to lift the cake out when cooled.
In a small non-stick saucepan, melt the chocolate, 4 tbsp of the milk, and the soft brown sugar together over a medium heat. Once melted, stir in the remaining milk.
In a free-standing mixer, or with a hand whisk, cream together the softened butter and caster sugar. Once pale in colour, beat in the egg yolks one at a time.
Add the flour, cocoa and bicarb to the mixture and beat until smooth. Pour in the melted chocolate mixture and beat until combined.
Using a clean whisk and a separate bowl, whisk the egg whites until stiff. Add in a couple of large spoons of the whisked egg white mixture into the main bowl, stir to combine and loosen the mix. Then gently fold in the remaining whisked whites, trying to maintain as much air as possible.
Pour the cake mix into the tin and bake in the pre-heated oven for 45 minutes.
Remove from the oven and leave to cool on a wire rack.
In the meantime, make the icing by melting the butter and milk in a small non-stick saucepan.
Remove from the heat and sift over the icing sugar and cocoa and beat well. Pour the icing over the cake and leave to cool before removing from the tin and slicing into 12 pieces.
Notes
The cake can be served at room temperature or warmed very slightly. Add some double cream, ice cream, or creme fraiche if desired.
This chocolate fudge cake will keep in an airtight container at room temperature for 3-5 days
You can freeze this cake either as a whole or in individual slices. It can be frozen for up to 3 months. To thaw the cake slices, leave at room temperature for 3-4 hours. If you are freezing the entire cake it will likely take a little longer. Once defrosted, you can always gently warm it (in a microwave for example) to soften the icing further.