Preheat the oven to 180°C. Grease and base-line 2x20cm sandwich tins. To make the marzipan, put the pistachios in a food processor and blend until finely ground. Add the almonds, caster sugar, icing sugar and the egg white and blend to a paste.
For the cake, put the butter, sugar, lemon zest, eggs, flour and baking powder in a bowl and beat with a hand-held electric whisk until pale and creamy. Beat in the lemon juice and spoon a quarter of the mixture into each of the tins. Level the surface.
Halve the pistachio marzipan and roll out each on a surface dusted with icing sugar until slightly smaller than the tins. Press gently over the sponge filling and cover with the remaining mixture. Bake for 35-40 minutes or until risen and just firm to the touch.
Loosen the edges of the cakes with a knife and transfer to a wire rack to cool.
For the icing, beat the butter with the icing sugar until light and fluffy. Beat in the lemon juice and use to sandwich the cakes together on a serving plate. Dust the top lightly with icing sugar and scatter with chopped pistachios to decorate. Cook's tip: Try swapping the butter icing for softly whipped cream swirled with a spoonful of lemon curd. Keep chilled and eat on the same day.