Grate the courgette into a bowl, keeping the stalk end on for easier handling.
In another bowl, combine the self-raising flour, baking powder, and sodium bicarbonate, mixing them well.
In the bowl with the courgette, add the caster sugar, eggs, and Mellow Yellow cold pressed rapeseed oil, then mix everything together thoroughly.
Gradually incorporate the flour mixture into the courgette mixture, stirring until well combined.
Divide the batter evenly between two lined baking tins.
Bake in a preheated oven at 160°C for about 30 minutes, or until the cakes are slightly browned and firm to the touch.
Allow the cakes to cool in the tins for a few minutes before transferring them to a wire rack to cool completely.
Finely grate the lime zest and squeeze the lime juice into a bowl.
Sift the icing sugar into another bowl, then add the cream cheese, lime juice, and lime zest, mixing thoroughly until thickened.
Spread just under half of the icing on the bottom layer of the cake, then swirl the remaining icing on top.
Sprinkle with pistachios for decoration and let it chill in the fridge for a few hours before serving.
