1. Make the Pastry Cream:

1. In a saucepan, heat milk over medium heat until steaming but not boiling.
2. In a separate bowl, whisk sugar, cornstarch, and egg yolks until smooth.
3. Gradually pour the hot milk into the egg mixture, whisking constantly.
4. Return the mixture to the saucepan and cook over medium heat, whisking continuously until thickened.
5. Remove from heat and whisk in butter and vanilla extract.
6. Transfer to a bowl, cover with plastic wrap (press directly on surface), and refrigerate for at least 3 hours.

2. Make the Cake:

1. Preheat oven to 350°F. Grease and flour two 9-inch round cake pans.
2. In a bowl, whisk flour, baking powder, and salt.
3. In another bowl, beat eggs, sugar, and vanilla until thick and pale.
4. Gradually add the flour mixture to the eggs.
5. Slowly pour in the hot milk and melted butter, mixing until just combined.
6. Divide batter between pans and bake 25–30 minutes or until golden and a toothpick comes out clean.
7. Cool in pans for 10 minutes, then transfer to wire racks to cool completely.

3. Make the Chocolate Glaze:

1. In a saucepan, heat cream and corn syrup until just simmering.
2. Remove from heat and stir in chopped chocolate.
3. Let sit 2 minutes, then stir until smooth.
4. Add vanilla extract and stir to combine.

4. Assemble the Pie:

1. Place one cake layer on a serving plate.
2. Spread chilled pastry cream evenly on top.
3. Add second cake layer.
4. Pour chocolate glaze over the top, letting it drip slightly down the sides.
5. Chill for 30 minutes before serving.