Preheat the oven to 350 degrees F and grease and line a cake tin 8 inches in diameter and 2 inches high.
Separate the yolks from the egg whites. Cream the yolks and sugar together until pale yellow and hanging like ribbons from the beater. Add the bread crumbs, ground coffee, cocoa and walnuts and mix well together. Whisk the egg whites stiffly and carefully fold into the walnut mixture. Pour the mixture into the prepared cake tin and bake for 45 minutes. Cool in the tin, then turn out onto a rack.
To make the icing, cream the butter with the icing sugar and egg yolk. Dissolve the instant coffee in the boiling water and mix well into the icing. Spread over the cake with a wet knife.