Preheat the oven to 160°C fan / 180°C conventional / 355°F. Grease and line two 20 cm (8-inch) round cake tins with baking paper.
In a large mixing bowl, beat the butter and sugar together for 3–5 minutes until pale, fluffy, and mousse-like.
Add the vanilla extract and mix until combined.
Add the eggs one at a time, beating well after each addition until the mixture is smooth.
Using a food processor, grind the pistachios into a fine crumb similar to almond meal.
Sift the flour and baking powder into the bowl. Add the salt and ground pistachios.
Gently fold everything together until just combined. Do not overmix.
Divide the batter evenly between the prepared cake tins and smooth the tops.
Bake for approximately 35 minutes, or until a skewer inserted into the center comes out clean.
Cool in the tins for 15 minutes before transferring to a wire rack to cool completely.
Prepare the Buttercream
Beat the softened butter and sifted icing sugar together until light and fluffy.
Add the pistachio cream, sea salt, and lemon juice.
Beat until smooth and creamy. Taste and adjust the lemon juice if desired.
Assemble the Cake
Place one cake layer on a serving plate.
Spread or pipe half of the pistachio buttercream evenly over the cake.
Carefully spread the raspberry jam over the buttercream, leaving a small border around the edge.
Place the second cake layer on top.
Cover the top with the remaining buttercream.
Decorate
Arrange fresh raspberries on top.
Sprinkle with chopped pistachios and garnish with fresh mint sprigs.
Slice and serve.