How to Make the Cake:
Sift the flour, sugar, baking powder, and salt into a large bowl.
Mix in the lemon zest with a fork, breaking up any clumps.
In a stand mixer fitted with the paddle attachment, combine the cream cheese, butter, and vanilla and beat on medium-high speed until smooth and slightly airy, 2 to 3minutes, stopping to scrape down the sides of the bowl as needed.
Add half the eggs (it may look a little curdled at first, but keep beating), then add the remaining eggs and the lemon juice and beat until well combined and smooth, scraping down the sides of the bowl as needed.
With the mixer on low speed, add the flour mixture in three batches, gently beating until just combined after each addition, scraping down the sides as needed.
Pour the batter into the prepared pan and smooth the top using an offset spatula. To release air bubbles, gently tap the pan on the counter.
Bake until the cake is golden brown and a toothpick inserted into the center comes out clean or with a few crumbs attached, about 1 hour 15 minutes. Let cool in the pan on a wire rack for 15 minutes.
Place a plate over the top of the pan and carefully invert the plate and pan together to turn the cake out onto the plate. Lift the pan and let cool for up to 2 hours.