Preheat the oven to 180C/350F/Gas 4.
In a bowl, beat the butter and sugar together until very light and pale.
Add the eggs and olive oil to the butter and sugar mixture, beating well to completely incorporate each egg before adding the next egg.
Add the espresso to the mixture and stir well.
Add the flour and walnuts and stir well to completely combine.
Spoon the cake mixture into two lined and greased 20cm/8in cake tins.
Transfer to the oven to bake 25-30 minutes, or until a skewer inserted into the centre of the cake comes out clean and the cake is golden-brown.
Remove the cakes from the oven and leave to cool on a wire rack.
For the buttercream topping, beat the butter and icing sugar together in a small bowl until pale and light.
Add the espresso and mix well.
Spread the buttercream over the top of each cake, then place one cake on top of the other.
Decorate the top of the cake with the walnut halves and serve in generous slices.