Preheat oven to 350 degrees F. Line bottom of a springform pan with parchment paper and grease the sides with butter.
Prepare the pistachio layer:
Add flour, pistachios, and powdered sugar to food processor. Process until pistachios are fine and ingredients are well combined. Add the butter, salt, and LorAnn Pistachio flavor. Process until dough forms, about 10 seconds. Press evenly into the base of the springform pan.
Prepare the cake layer:
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.
To make glaze:
Whisk together powdered sugar, lemon juice and lemon zest. Add small amounts of warm water until your desired consistency is achieved.
Once the cake is entirely cool, remove it from the pan and pour the glaze over the top, spreading to the sides to allow it to drizzle over.