This cake is simple to make, but it's ridiculously sophisticated in flavor. I add a touch of cardamom to round out the sweetness, and the texture is an absolute dream: moist and almost chewy but still delicate and light. If you want, you can easily use all pistachios (100 grams) or all almonds (100 grams). —Posie (Harwood) Brien
Preheat the oven to 350°F. Line a 9" cake pan with parchment paper, lightly grease the pan, and dust it with sugar, tapping out the excess sugar.
In a food processor, pulse together the pistachios until they're fairly finely ground, but make sure not to pulse too much or they'll become a paste.
Add the almond flour, all-purpose flour, baking powder, and cardamom to the ground pistachios and pulse until everything is combined.
In the bowl of a stand mixer, beat the eggs with the sugar until very thick and light and fluffy, about 5 minutes.
Slowly drizzle the olive oil into the egg/sugar mixture, beating as you go. Once combined, keep the mixer running on low and drizzle in the melted butter (if you don't have salted butter, add 1/2 teaspoon of salt with the butter). Beat until the mixture comes together, but don't overmix as you want to keep as much air in the batter as possible.
Gently fold the dry ingredients into the wet, taking care not to deflate the batter as much as possible. Once combined, pour the batter into the prepared cake pan and smooth the top.
Bake for about 45-55 minutes, or until the sides of the cake turn golden and a cake tester inserted into the center comes out clean or with just a few moist crumbs. Let the cake cool completely in the pan before turning it out onto a rack to slice.