Preheat oven to 180 C / Gas 4. Lightly grease two 23x13cm loaf tins.
Mix flour, bicarbonate of soda and salt in a bowl. Beat eggs, sugar and vegetable oil together in another bowl; stir in yogurt, lemon zest, lemon juice and vanilla extract. Gradually stir flour mixture into wet ingredients until just moistened; fold grated courgette and chopped pistachios into the mixture. Pour the cake mix evenly into prepared loaf tins.
Bake in the preheated oven until a skewer inserted into the centre comes out clean, 45 to 55 minutes. Cool in loaf tins for 10 minutes before removing to cool completely on a wire cooling rack.