Prepare the Pistachios: Start by pulsing the pistachios in a food processor until finely ground. Stop before they turn oily. This gives the cake its signature flavor and soft texture. Set them aside.
Get the Oven Ready: Heat the oven to 170°C. Grease and line a round cake tin with baking paper. This helps the cake bake evenly and release cleanly.
Mix the Dry Ingredients: In a bowl, whisk together flour, baking powder, baking soda, salt, and the ground pistachios. Mixing now spreads everything evenly through the batter.
Combine the Wet Ingredients: In another bowl, mix yogurt, melted butter, oil, caster sugar, egg, vanilla, and food colouring. Stir until smooth and lightly glossy.
Bring the Batter Together: Add the dry mixture to the wet ingredients. Fold gently until just combined. The batter should look thick and smooth with a soft green color.
Bake the Cake: Pour the batter into the prepared tin and smooth the top. Bake for 40 to 45 minutes until the top feels set and a skewer comes out clean. Let it cool fully before topping.
Make the Creamy Topping: Beat the cream cheese until smooth. Add cream, sugar, vanilla, lemon juice, and salt. Whip until light and softly thick. Spread over the cooled cake.