Preheat the oven to 180°C/160°C Fan/gas mark 4/350°F.
Butter two 8inch sandwich tins and line the base of each with baking parchment. Alternatively, use one larger tin, and slice the cakes in half once baked.
Put the walnut pieces into a food processor and blend to almost a fine powder.
Add the flour, butter, espresso, baking powder, bicarbonate and eggs into a large bowl or stand mixer. Process to a smooth batter.
Add the milk, pouring it down the funnel with the motor still running, or just pulsing, to loosen the cake mixture until you reach a light and creamy consistency.
Divide the mixture between the 2 your two cake tins and bake in the oven for 25 minutes, or until the sponge is pulling away from the sides and feels springy to the touch.
Cool the cakes in their tins on a wire rack for about 10 minutes, before turning them out onto the rack and peeling off the baking parchment.
When the sponges are cool, you can make the buttercream.