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Heat the oven to 180C/160C fan/ gas 4. Oil a 900g loaf tin and line with baking parchment. Combine the sugar, oil and eggs in a large bowl and mix well. Fold in the flour, baking powder and ground pistachios. Squeeze out as much moisture as you can from the grated courgette using your hands (don’t worry about squeezing out every drop), then add this to the bowl along with the lime zest and half the juice, and mix to combine.
Bake for 40-50 mins until a skewer inserted into the middle comes out clean. Check the cake after 30 mins – if it’s looking too brown, cover with foil for the remaining cooking time. Leave to cool in the tin for 20 mins, then transfer to a wire rack, poke a few holes in the top using a skewer and pour over the remaining lime juice. Leave to cool completely. Once cool, will keep frozen for up to a month. Defrost fully before decorating and serving.
For the frosting, tip the soft cheese into a bowl, sift over the icing sugar, pour in the lime juice and mix to combine. Spread this over the top of the cooled cake, then sprinkle with the chopped pistachios and lime zest. Will keep chilled in an airtight container for up to three days.
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