Prepare the Custard Filling:

• Whisk together egg yolks, sugar, flour, and cornstarch until smooth in a medium bowl.
• In a saucepan, heat the milk and remaining sugar over medium heat until steaming but not boiling.
• Gradually pour the hot milk into the egg mixture, whisking constantly.
• Return the mixture to the saucepan, stirring continuously, and cook until thickened and boiling.
• Remove from heat, stir in vanilla extract and butter until smooth.
• Transfer the custard to a bowl, cover with plastic wrap touching the surface, and refrigerate until completely cooled.

Prepare the Vanilla Sponge Cake:

• Preheat the oven to 335°F (170°C). Grease and line two 8-inch round cake pans with parchment paper.
• Sift together cake flour, baking powder, and salt in a large bowl.
• In another bowl, cream together the butter and sugar until light and fluffy.
• Add eggs one at a time, beating well after each addition.
• Mix in vanilla extract.
• Alternately add the dry ingredients and milk to the batter, starting and ending with the dry ingredients.
• Divide the batter evenly between the prepared pans and smooth the tops.
• Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
• Allow the cakes to cool in the pans for 10 minutes before transferring to a wire rack to cool completely.

Prepare the Custard Buttercream:

• Beat the butter until creamy and pale in a large bowl.
• Gradually add powdered sugar, beating until smooth and fluffy.
• Mix in the cooled custard and vanilla extract until fully combined.

Assemble the Cake:

• Level the cooled cakes if necessary.
• Place one cake layer on a serving plate and spread a layer of custard buttercream on top.
• Add a layer of custard filling over the buttercream.
• Place the second cake layer on top and spread the remaining custard buttercream over the top and sides of the cake.
• Refrigerate for at least 1 hour before serving to allow the layers to set.