Place the lemon juice, room-temperature egg yolks, granulated sugar, salt, and finely grated lemon zest in a medium saucepan.
Whisk the ingredients thoroughly until they form a uniform mixture.
Set the saucepan over medium-low heat and cook for 20–25 minutes, stirring frequently. Continue until the curd has thickened enough to coat the back of a spoon.
Take the pan off the heat. Gradually whisk in the cubes of cold unsalted butter, allowing each addition to melt completely into the curd.
Transfer the finished lemon curd to a heatproof bowl. Press plastic wrap directly against the surface to prevent a skin from forming, then refrigerate until thoroughly chilled.
Preheat the oven to 350°F (175°C).
Coat a 9 × 9-inch baking pan with non-stick cooking spray, then line it with parchment paper.
In a medium mixing bowl, whisk the all-purpose flour with the baking powder, baking soda, and salt until evenly distributed.
In a separate large bowl, use an electric mixer to beat the softened butter and granulated sugar together for approximately 2 minutes, until well creamed.
Add the room-temperature eggs and vanilla extract. Beat at medium speed for about 1 minute, or until the mixture becomes smooth and pale.
With the mixer operating on low speed, gradually alternate additions of the dry flour mixture and room-temperature buttermilk into the butter mixture. Mix only until the cake batter is combined.
Scrape down the sides and bottom of the bowl with a rubber spatula whenever necessary to ensure the batter is evenly mixed.
Carefully fold the 3 tablespoons of lemon zest into the completed batter.
Transfer the batter to the prepared 9 × 9-inch pan and spread it evenly.
Bake for 35–40 minutes. The cake is ready when a toothpick inserted into the center comes out clean.
Place the pan on a wire cooling rack and allow the cake to cool completely before filling and frosting.
While the cake is cooling, place the softened butter in a large mixing bowl. Beat it with an electric mixer on high speed for approximately 5 minutes, until noticeably pale and fluffy.
Add the cold cream cheese and continue beating on high speed for about 1 minute, until the mixture is light and evenly blended.
Sift the powdered sugar into the bowl. Begin mixing at low speed to incorporate it, then increase to high speed and continue beating until the frosting becomes fully combined and fluffy.
Add the ½ tablespoon of lemon zest and whip once more until evenly incorporated and airy.
Once completely cool, carefully remove the cake from its pan and place it on a serving platter.
Using the handle of a wooden spoon or a thick skewer, make holes evenly across the entire surface of the cake.
Spoon the chilled lemon curd into a piping bag and pipe the curd directly into the prepared holes.
Using an offset spatula, spread a thick, even covering of lemon cream cheese frosting across the top of the cake.
Finish by swirling additional lemon curd through the frosting to create a tangy lemon topping.
Slice and serve.