Preheat the oven to 170ºC. Line the bottom of two 22cm round cake tins with parchment paper and grease the sides lightly with butter.
In a large mixing bowl, using an electric whisk, cream together the butter and sugar until light and fluffy. The butter should be soft and a light golden colour.
Add in the eggs and whip together. Make sure that the eggs are fully incorporated, then add in the cooled coffee. Whisk one more time. The mixture may look curdled, but it will come back together once you add the flour.
Sift the flour and baking powder into the egg and butter mixture. Add in the chopped walnuts and milk. Being careful not to over mix, make sure that the flour is fully combined.
Divide the batter between the two lined cake tins and bake in the preheated oven until the tops spring back when gently pressed and a toothpick or skewers comes out with a few moist crumbs. About 18 minutes.
Once the cakes are baked, allow them to cool in the tins on a cooling rack for about 10 minutes before turning out to cool completely.
To make the frosting
Whip the butter and cream cheese together until very light and fluffy. Sift in the icing sugar and whip again. See notes. Slowly pour in the cooled coffee and whip until silky smooth and creamy.
Frost the bottom layer of cake. Place the second sponge on top and frost that. Sprinkle the chopped walnuts around the edge of the cake and serve.