Boston Cream Pie Birthday Cake is a vanilla butter cake with a pastry cream filling and chocolate ganache topping.
Preheat oven to 350°F. Grease and line with parchment paper 2 (9-inch) round cake pans. (I used non-stick cooking spray before and after placing a parchment paper circle which I cut out myself after tracing the line of the pan onto the paper.) Set aside.
Place cake flour, baking powder and salt in a medium bowl. Whisk until combined. Set aside.
In a large bowl, beat butter and sugar with an electric mixer on medium until light and fluffy, about 2 minutes. With mixer on low, gradually add eggs (one at a time). Turn mixer to medium and beat for 30 seconds or until eggs are completely mixed in.
Combine milk and vanilla in a small bowl, then with mixer on low, alternate adding milk mixture and flour mixture. Add about a third of the flour, then a third of the liquid. Mix until combined. Repeat with remaining dry and wet ingredients. Once all of the cake ingredients are combined, turn mixer up to medium and beat for about 30 seconds.
Pour batter into prepared pans, dividing the batter equally between the two. Bake for 30-35 minutes or until a toothpick inserted into the middle comes out clean. Let cool.
In a medium sized, heavy saucepan, add sugar, cornstarch and salt. Stir to combine. Gradually add milk, stirring constantly. Add egg yolks and whisk together. Turn heat to medium and keep whisking. Let it come to a boil, whisking all the while. Once it comes to a boil, keep whisking for 1 minute or until thick. Remove from heat. Stir in vanilla. Let cool slightly, then pour into a medium bowl. Cover with plastic wrap, letting it touch the top of the custard to prevent it from crusting. Set aside.
Place butter and chocolate in a small, heavy saucepan. Turn the heat on low and let it melt, stirring constantly. Remove from heat and let cool about 3-4 minutes. Add powdered sugar and boiling water. Stir with a wooden spoon until smooth.
Place one layer of cake on a serving plate. Spread custard on top. Add second layer of cake. Pour chocolate ganache on top, spreading it quickly so that some of it drips down the sides. Refrigerate at least one hour before serving. Slice and serve. Store leftover cake covered in refrigerator.