Preheat oven to 175°C, and grease and line a cake tin with baking paper.
In a food processor or blender, blitz the pistachios to a fine meal.
Cream butter and caster sugar in a stand mixer until light and fluffy. Add eggs, one at a time, beating until well combined. Fold through the ground almonds, finely ground pistachios, all-purpose flour, baking powder and vanilla.
Pour the batter into the tin and smooth the surface. Top with plum halves, cut side up.
Bake for 45-50min or until a skewer inserted comes out just clean. Leave in the tin to cool.
To glaze, mix together the icing sugar and lemon juice until desired consistency. Drizzle over cake and top with chopped pistachios.