Preheat the oven to 160°C fan (180°C conventional, 355°F). Grease and line two 20 cm (8-inch) round cake pans with parchment paper.
In a large mixing bowl, beat softened butter and sugar for 3 to 5 minutes until pale, fluffy, and mousse-like. Mix in vanilla extract.
Add eggs one at a time, beating well after each addition until the batter is smooth.
Process pistachios in a food processor until finely ground like almond flour.
Sift together flour and baking powder. Add salt and ground pistachios. Fold the dry ingredients gently into the wet mixture until just combined.
Divide the batter evenly between the prepared pans and smooth the tops. Bake for 35 minutes or until a skewer inserted into the center comes out clean.
Allow cakes to cool in pans for 15 minutes, then transfer to a rack to cool completely.
For the buttercream, beat softened butter and powdered sugar until pale and fluffy. Add pistachio cream, salt, and lemon juice, then beat again until smooth.
To assemble, place one cake layer on a serving plate. Spread half the buttercream evenly over the top, then gently spread raspberry jam on top of the buttercream.
Place the second cake layer on top and cover with the remaining buttercream.
Decorate the cake with fresh raspberries, mint sprigs, and chopped pistachios.