Heat the oven to 180C/350F/gas 4. Grease and line a 450g loaf tin.
Put the pistachios on a baking tray and roast for seven to eight minutes until they are beginning to turn golden, then remove and leave to cool. Once cool, empty into a food processor and blitz until they are the texture of breadcrumbs. Set aside 30g for garnishing the cake later.
Put the oil and sugar into the bowl of a stand mixer and beat until thick and creamy. Add the eggs, one at a time with the machine running moderately slowly, then carefully fold in 70g of the pistachios, the flour, a pinch of salt, the courgettes and the lemon zest. Do not overmix, or the cake will become heavy.
Pour the cake mixture into the prepared tin and bake in the oven for 65-75 minutes, or until an inserted skewer comes out clean.
While the cake is baking, make the drizzle. Warm the sugar in a pan over a medium heat until dissolved, then add the lemon juice and stir. As soon as you have removed the cake from the oven, prick it all over with a cocktail stick and pour over the warm syrup so it runs into the holes. Scatter over the reserved pistachios, followed by the lemon zest. Leave to cool, then remove from the tin and serve in thick slices with dollops of creme fraiche, softly whipped double cream or a dairy-free substitute.