Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a mixing bowl, whisk together flour, sugar, baking powder, and salt.
In another bowl, mix milk, melted butter, vanilla extract, and eggs. Add to the dry ingredients and mix until smooth.
Pour batter into prepared pans and bake for 25-30 minutes or until a toothpick inserted into the center comes out clean. Let cakes cool on a wire rack.
For the custard, heat milk in a saucepan until simmering. In a bowl, whisk sugar, cornstarch, and egg yolks. Slowly add hot milk to the egg mixture, then return to the saucepan. Cook over medium heat until thickened. Remove from heat and stir in butter and vanilla. Let cool.
For the glaze, heat heavy cream until simmering. Pour over chopped chocolate and let sit for 5 minutes. Stir until smooth.
To assemble, place one cake layer on a serving plate. Spread custard over the top. Place the second cake layer on top. Pour chocolate glaze over the top, letting it drip down the sides. Refrigerate until set.