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Preheat your oven to 180°C/350°F (fan-forced).
In a large mixing bowl, combine the olive oil, sugar, lemon zest, and vanilla, whisking well until everything is mixed together.
Add the eggs and whisk until the mixture is smooth and well combined.
Gently fold in the yoghurt and lemon juice until the mixture is smooth.
Pour the batter into a pre-lined 23cm/9inch round cake tin.
Bake for 45 minutes, or until a skewer inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool completely. You can speed up the cooling process by placing the cake in the freezer for an hour or two before icing.
In a separate bowl, beat the cream cheese and vanilla until smooth.
Add the icing sugar and lemon juice, and continue to beat until the mixture is very smooth.
Set the frosting aside until you are ready to use it.
Once the cake is completely cooled, place it onto a serving plate.
Spread the frosting over the top of the cake, smoothing it out to the edges with the back of a spoon.
Create large swooshes on the top of the frosting using the back of the spoon.
Finish by topping the cake with lemon zest and finely chopped pistachios.