1 Preheat the oven to 170C¼/gas mark 3. Grease the tin and line the base with baking parchment.
2 Melt the butter with the olive or pistachio oil in a small saucepan over a low heat. Remove from the heat and leave to cool slightly.
3 Whizz the pistachios in a food processor until they are very finely chopped. Add the coconut, flour, baking powder and salt and whizz for no more than 10 seconds, just to combine.
4 Using an electric mixer, whisk the eggs and sugar on medium–high speed until they are very thick and pale, trebled in volume and leave a ribbon trail when the whisk is lifted from the bowl.
5 Gently fold in the lime zest and pistachio mixture using a large metal spoon, then fold in the butter mixture and soured cream. Pour into the tin, spread level and bake on the middle shelf of the oven for 40–50 minutes or until a wooden skewer inserted into the middle comes out clean.
6 Meanwhile, prepare the syrup. In a small saucepan, bring the lime juice, agave syrup or honey, sugar and 200ml of cold water to the boil. Continue to bubble steadily until reduced by half and syrupy.
7 Leave the cake to cool in the tin on a wire rack for 5 minutes, then carefully run an off-set palette knife around the edge of the cake to release the sides from the tin. Using the wooden skewer, make holes all over the top of the cake while it is still in the tin, then either slowly drizzle or carefully brush half the syrup all over the warm cake. Set aside until completely cold.
8 Tip the berries into the remaining syrup and return to a low heat for a couple of minutes to slightly soften them. Remove from the heat, spoon into a bowl and leave to cool.
Serve the cake in slices with fromage frais, creme fraiche or Greek yogurt and the berry compote spooned over.
Summer Berries and Autumn Fruit by Annie Rigg. Published by Kyle Books, priced £19.99.
Photography by Tara Fisher.