Cream the butter and sugar until light and fluffy.
Then add the coffee essence and mix until well distributed.
Add the eggs, gradually, beating well between each addition.
Fold in the flour and then the walnuts.
Spoon the mixture into a lined 2lb loaf tin and bake for approximately 45 minutes, or until a skewer comes out clean.
Remove from the oven and let cool briefly before lifting out onto a wire rack to cool.
For the buttercream, cream the butter and sugar until light and fluffy, then add the milk and coffee. Spread over the top of the cake and scatter with walnuts.