Preheat the oven to 150C/300F/gas 2. Line a dish or tin measuring about 33cm x 23cm with baking parchment.
Half-fill a pan with water and put it on a high heat to boil, then reduce to a simmer. Break the chocolate into pieces and put it, with the butter, into a large bowl. Place the bowl above but not touching the simmering water and let the butter and chocolate melt.
Crack the eggs into another large bowl and add the sugar. Beat until pale and voluminous. In a separate bowl, sift together the flour and cocoa.
When the butter and chocolate are quite melted, gently add this to the beaten eggs and sugar. Mix deftly, then add the sifted flour and cocoa. A swift but thorough mixing is required. Decant this into the lined baking dish.
Put in the oven and bake for 30-35 minutes. Check for doneness by inserting a knife or a skewer. A trace of wet chocolate gooeyness is good. Remove the tray to a cooling rack.
To make the fudge sauce, put all the ingredients except the chocolate into a large, heavy-based pan. Put the pan on a moderate heat and bring to a simmer. Stir well and cook gently for about 10 minutes. Break the chocolate into pieces and beat into the fudge. Remove from the heat and stir gently until smooth.
Check on the cooked brownie – it should be reasonably flat.
Pour on enough fudge sauce to generously ice the whole tray of brownie.
Let the fudgy brownie now sit. The longer the better – a few hours preferably. When ready, cut 20 rough squares from the brownie, say 5 squares along one side, 4 along the shorter side. Lift each square on to a tray, popping a walnut half into the fudge in the middle of each.