Preheat the oven to 180'C.
Butter a cake tin and line with baking parchment.
Zest and juice the lemon.
Sift the flour and baking powder together.
In a bowl, beat the sugar and the butter together until pale and fluffy. One at a time, beat the eggs into the mixture before adding the oil, vanilla, chopped pistachios and the zest and juice of the lemon. Gently fold in the flour and then pour the mixture into the cake tin.
Transfer to the oven and bake for 30 minutes. Check the centre of the cake with a skewer or the tip of a sharp knife - if the skewers comes out clean, the cake is ready. Return the cake to the oven for a further 10 minutes if necessary.
Heat the apricot jam in a saucepan and pour it over the cake. Spread it over the cake to serve.
«Take care not to overwork the mixture once you have folded in the flour - you want to keep the air in the mixture to prevent the cake from becoming dense once baked.»