Prepare the pistachio cake batter

• Heat the oven to 180 °C (350 °F) and grease three 6-inch cake pans.
• Blitz the pistachios in a food processor until finely ground.
• Whisk the flour, ground pistachios, baking powder, baking soda and salt in a bowl.
• Whisk the melted butter, sugar, eggs, yogurt, oil and vanilla in another bowl, then fold in the dry ingredients until just combined.

Bake the cake layers

• Divide the batter evenly between the prepared pans.
• Bake until a skewer comes out clean.
• Cool in the pans briefly, then turn out onto a cooling rack to cool completely.

Make the raspberry jam

• Combine the raspberries, sugar and water in a saucepan.
• Simmer, stirring and mashing the fruit, until thick and jammy.
• Pass through a sieve to remove the seeds and let cool.

Make the raspberry buttercream

• Beat the softened butter in a stand mixer until pale and fluffy.
• Add the powdered sugar and beat until smooth.
• Mix in the raspberry jam, vanilla and heavy cream and beat until light and spreadable.

Assemble the cake

• Place the first cake layer on a cake stand and spread raspberry jam over it.
• Add a layer of raspberry buttercream, then top with the next cake layer and repeat.
• Cover the whole cake with a thin crumb coat of buttercream and chill.

Decorate the cake

• Cover the cake with a final layer of raspberry buttercream and smooth it.
• Pipe decorative vintage-style borders with the remaining buttercream.
• Finish with fresh raspberries and chopped pistachios.