Make the Cake
Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans. In a medium bowl, whisk together the flour, baking powder, and salt. In another bowl, beat the eggs and sugar until pale and fluffy. Add the vanilla extract, milk, and melted butter, and mix until combined. Gradually add the dry ingredients and stir until just incorporated.

Bake the Cake
Divide the batter evenly between the two prepared pans. Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 10 minutes, then turn them out onto a wire rack to cool completely.

Make the Custard Filling
In a saucepan, combine the milk, egg yolks, sugar, and cornstarch. Cook over medium heat, whisking constantly until the mixture thickens and comes to a boil. Remove from heat, then stir in the vanilla extract and butter. Let the custard cool slightly before using.

Assemble the Cake
Once the cakes are completely cooled, place one layer on a serving platter. Spread the custard filling evenly over the top. Place the second cake layer on top of the custard.

Make the Chocolate Ganache
Heat the heavy cream in a small saucepan over medium heat until it just begins to simmer. Pour the hot cream over the chopped chocolate and let it sit for 2-3 minutes. Stir until smooth, then mix in the butter until glossy.

Top the Cake
Pour the chocolate ganache over the top of the cake, letting it drip down the sides. Allow the ganache to set for about 30 minutes before slicing and serving.