Add cake flour, granulated sugar, baking powder, and salt to the bowl of a stand mixer. Combine well. With the paddle mixing on medium speed, add butter in small chunks until the entire mixture becomes uniform and crumbly. This takes about a minute and the flour should be well coated with the butter.
In a separate bowl, whisk together milk, eggs, oil, lemon zest and lemon juice.
With the stand mixer running on low speed, add just enough of the liquid mixture (shouldn't be more than half) to the flour to barely moisten the batter. Increase speed to medium and mix until light and fluffy, about 2 minutes. Scrape bowl, add remaining liquid, and mix on low speed until well combined, scraping as necessary.
Pour the cake batter on top of the pistachio layer.
Bake the cake for 45 minutes. Remove when it is set and a toothpick inserted comes out clean. Allow to cool in pan before removing.