Line a loaf tin with baking paper and pre-heat the oven to 170C/340F.
Whisk together the eggs, sugar, oil, yoghurt, vanilla essence, lime zest and juice in a large bowl.
Stir in the zucchini and then fold in the flour and baking powder and most of the pistachios (save a couple of tablespoons).
Pour the mixture into the loaf tin, then bake for 45 to 50 minutes or until the loaf is risen and golden and a skewer poked into the centre comes out clean. Then cool completely on a wire rack.
Meanwhile, make the icing. Beat together the cream cheese and butter, then add most of the lime zest and the juice. Finally, stir in the icing sugar. Keep adding more icing sugar until the icing seems thick enough to sit on top of the cake without sliding off!
When the cake is completely cool, spread the icing over the top. Decorate with the remaining pistachios and lime zest.