Preheat oven to 160oC.
Line and grease a 20cm springform cake tin.
Place the pistachios in a blender or food processor to grind them to a fine crumb.
Place sugar and oil in the large bowl of an electric mixer. Whisk for 2 minutes to dissolve the sugar. Add the eggs followed by the vanilla extract. Add the yoghurt and combine well. Fold in the flour, baking powder and ground pistachios.
Pour mixture into the prepared cake tin and bake for 45-50minutes or until your skewer comes out clean. Leave in tin to cool for 10 minutes and then take out of tin and cool completely on a wire rack.
o prepare the icing, sift the icing sugar into a bowl and blend to a smooth paste with the yoghurt. Pour icing onto cake and smooth it out and down the sides using a spatula (I usually take the lazier approach and let it drip down the sides which also looks quite lovely).
Allow small droplets of pomegranate juice to fall on the cake. You can let it find it’s own style or if you prefer to be more in control, use a toothpick to swirl loosely and gently to form your own pattern through the icing.
Scatter pomegranate seeds and roughly chopped pistachios on top of the cake and around platter to decorate.