Preheat the oven to 350F (177C) convection (325F/163C conventional) and grease and line four 6 inch cake pan with baking spray and parchment paper.
Place the fully dried pistachios in the bowl of a food processor and pulse at full speed for 2-3 minutes until they’re as ground as they’re going to get (don’t turn it into a paste).
1 1/2 cups (6oz/175g) pistachios
Add the cake flour, baking powder and salt to the food processor and let it run for a few more minutes at full speed until the pistachios just about blend into the flour mix.
2 cups (240g) cake flour, 1 Tbsp (10g) baking powder, 1/2 tsp salt
Place the room temperature butter and the granulated sugar in a large bowl and use an electric mixer with the whisk attachment to beat them for 2 minutes, scraping the edge of the bowl halfway through.
1/2 cup (113g/1 stick/4oz) unsalted butter, 1 1/2 cups (300g) granulated sugar
Add in the oil and beat for another 1-2 minutes, at full speed, until it's pale and fluffy.
1/4 cup (59mL) vegetable oil
Add the egg whites, 1-2 at a time, beating on medium speed between each addition for about 1-2 minutes, until each egg is fully incorporated and the batter is fluffy.
5 large
Add the vanilla extract and sour cream and beat just until they're combined.
2 tsp vanilla extract, 3/4 cup (170g) sour cream
Add half of the dry ingredients to the batter, turn the mixer up to low speed and stream in the half and half, followed by the rest of the dry ingredients.
3/4 cup (177mL/6oz) half and half
Spread the cake batter in the prepared cake pans and bake for 30 minutes, until it releases itself from the edge of the pan and/or springs back if you gently press on the center of it.
Flip over onto a tea towel and allow the cake to cool completely before frosting.