Preheat oven to 350°F (175°C). Grease and line an 8-inch round cake pan with parchment.
In a medium bowl, whisk together all-purpose flour, almond flour, ground pistachios, baking powder, and kosher salt.
In a large bowl, whisk eggs and sugar until light and foamy, about 2 minutes.
Add olive oil, sour cream, lemon zest, and vanilla extract. Whisk until fully combined.
Fold dry ingredients into the wet, mixing just until no dry streaks remain.
Pour into the prepared pan and smooth the top with a spatula.
Bake for 32–36 minutes, starting to test with a cake tester at 25 minutes. Cake is done when tester comes out clean or with moist crumbs.
Place the cake (still in pan) in the freezer for 20 minutes to set the crumb and retain moisture, or cool completely on a wire rack.