1. Preheat the oven to 350°F (175°C), grease two 9-inch round cake pans, and line them with parchment paper.
2. Cream together softened butter and sugar in a large mixing bowl until the mixture is light and fluffy.
3. Gradually beat in the eggs one at a time, ensuring each egg is fully incorporated before adding the next.
4. Sift together the flour, baking powder, and salt.
5. Alternately add the dry ingredients and milk to the creamed mixture, starting and ending with the flour. Mix until just combined, then stir in the vanilla extract.
6. Divide the batter evenly between the prepared pans, smooth the tops, and bake for 25 to 30 minutes until a toothpick inserted into the center comes out clean. Cool completely on a wire rack.
7. For the vanilla pastry cream, heat milk in a medium saucepan until it just starts to simmer, then remove from heat.
8. In a separate bowl, whisk together sugar, salt, and egg yolks until pale and thick. Add cornstarch and mix until smooth.
9. Gradually whisk half of the hot milk into the egg mixture to temper the eggs, then pour the mixture back into the saucepan with the remaining milk.
10. Cook over medium heat, continuously whisking until the pastry cream thickens and comes to a boil. Boil for 1 minute, then remove from heat.
11. Stir in vanilla extract and butter until fully integrated, then transfer to a bowl and cover with plastic wrap pressed against the surface to prevent a skin from forming. Let it cool completely.
12. For the chocolate glaze, place chopped chocolate in a heatproof bowl and heat heavy cream in a small saucepan until it just begins to simmer.
13. Pour the hot cream over the chocolate, let it sit for a minute, then stir until the glaze is smooth.
14. Once the cake layers and pastry cream are completely cooled, assemble the dessert by placing one cake layer on a serving plate and spreading the pastry cream evenly across the top.
15. Place the second cake layer on top of the pastry cream.
16. Pour the chocolate glaze over the top of the cake, allowing it to drip down the sides.
17. Chill the assembled Boston Cream Pie in the fridge for at least 30 minutes to set the glaze before slicing and serving.