Preparation:

Step 1: Prepare the Cake Layers

1. Preheat the oven to 350°F (175°C). Grease and flour three 9-inch round cake pans.
2. In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
3. In a large mixing bowl, cream the butter and sugar together until light and fluffy.
4. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
5. Alternately add the flour mixture and milk to the butter mixture, starting and ending with the dry ingredients. Mix until just combined.
6. Stir in the lemon juice and lemon zest.
7. Divide the batter evenly between the prepared cake pans and bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
8. Let the cakes cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.

Step 2: Make the Lemon Cheese Filling

1. In a saucepan, whisk together the sugar and cornstarch.
2. Stir in the fresh lemon juice and egg yolks.
3. Cook over medium heat, stirring constantly, until the mixture thickens and coats the back of a spoon (about 8-10 minutes).
4. Remove from heat and stir in the butter and lemon zest until smooth.
5. Let the filling cool completely before using.

Step 3: Prepare the Lemon Frosting

1. Beat the butter in a large bowl until smooth and creamy.
2. Gradually add the powdered sugar, mixing well after each addition.
3. Stir in the lemon juice and zest.
4. Add heavy cream, one tablespoon at a time, until the frosting reaches a spreadable consistency.

Step 4: Assemble the Cake

1. Place one cake layer on a serving plate and spread a generous amount of the lemon cheese filling on top.
2. Repeat with the second cake layer and more lemon filling.
3. Place the final cake layer on top and frost the entire cake with the lemon frosting.

Step 5: Chill and Serve

1. Refrigerate the cake for at least 1 hour before serving to allow the flavors to meld.
2. Slice and enjoy!