Bring a pot filled halfway with water to a simmer. Pour in the raw pistachios; heat for 3-5 minutes, stirring often. Pour the nuts through a fine mesh sieve to discard the water. Place the nuts in the center of a clean flour sack or tea towel and fold the towel over the middle then press and roll the towel so the nuts rub against each other, this will help loosen the skins.

Have a seat now! One by one, peel the purple/brown skin off the pistachios. Discard the skin. (You can do this step ahead of time but the nuts may turn brown due to oxidation.)

Once all are peeled, preheat the oven to 350 F. Set the pistachios on a small rimmed baking sheet and toast for about 10 minutes, until fragrant. Transfer to a strong blender and blend on high; the nuts will first turn into a powder but blend them for another 5 minutes afterwards until it starts to thicken. Add the olive oil into the food processor and blend until smooth, a few minutes should do it.

Preheat the oven to 325 F and grease and flour two round 8 inch cake pans.

Add the sugar to a stand mixer bowl or a large bowl (to use a hand mixer) and zest the lemons over it. Rub the zest into the sugar with your fingers.

Add the vanilla, salt and eggs. Beat with the paddle attachment until light and fluffy, about 5 minutes.

With the mixer on, slowly pour in the pistachio olive oil mixture and continue beating until well combined.

Sift in the cake flour and add the baking powder. Turn the mixer on, and while it’s beating, pour in the buttermilk.

Scrape the bowl down the sides and bottom to ensure even mixing. When the batter is even, divide it between the two prepared pans.

Bake until the top springs back when pressed or a cake tester comes out clean, about 30-40 minutes.

Transfer to a cooling rack and let cool completely.

Set the room temperature cream cheese and butter in a large bowl (use a stand mixer or a hand mixer). Use a wooden spoon or large rubber spatula to press down on the cream cheese to remove any lumps.

Add the vanilla and salt and beat until smooth. Add in the pistachio paste and beat to combine. (Careful not to overdo it, over whipped cream cheese can become soupy.)

Pour in the powdered sugar and beat until smooth.

To stack and frost the cakes: slice off the domes on the cakes and place one cake face up. Spread a layer of frosting over the top of it then place the second cake face down. Spread frosting over the top and around the sides. Sprinkle crushed pistachios on top, if desired.

The cake keeps very well for 3-4 days if kept in an airtight container.