Heat the oven to 180C/170C fan/gas mark 4. Oil a 900g (2lb) loaf tin and line with baking parchment. Line the base with a long piece so that it overhangs the shorter ends of the tin; this makes it easier to lift out the cake.
Put 100g pistachio kernels in a food processor and lightly pulse (if you grind them too much or too fast, the oil comes out and the nuts clump – you don’t want that).
Put the nuts in a large bowl with 200g soft light brown sugar, 200g self-raising flour and the finely-grated zest of 2 limes. Mix together to combine.
Put 200ml light olive oil, 2 large eggs, 75g Greek yoghurt, 1 tsp vanilla extract and the juice of 2 limes into a jug or bowl and stir it all together until combined.
Squeeze the water from 200g coarsely-grated courgettes using your hands or a clean J-cloth.
Add the courgettes and the wet ingredients to the dry mixture, stirring with a fork. There shouldn’t be any trace of flour left unincorporated.
Scrape the batter into the prepared tin and bake for about 1 hour 15 minutes, or until a skewer pushed into the middle of the cake comes out clean.
Leave to cool for 15 minutes then turn out onto a wire rack.
Leave the cake to cool completely while you make the buttercream.
Beat 70g butter until soft. Slowly add 150g icing sugar (if you don’t add it slowly the sugar billows everywhere).
Once you have a lovely silky buttercream, mix in the finely-grated zest of 1 lime, then add the juice of the lime slowly (if you add it all at once the buttercream can curdle).
When the cake is at room temperature, spread the buttercream on top using a palette knife. Scatter 50g chopped pistachios on top.
This will be fine, loosely wrapped in foil, for several days (if you can manage not to eat it).
