Pour the milk into a medium-sized saucepan set over medium heat to simmer.
2¼ cup milk
While the milk is heating up, place the egg yolks, sugar, cornstarch, and salt in a medium-sized bowl. Whisk well until combined and smooth.
7 egg yolks, ¾ cup granulated sugar, 5 tablespoons cornstarch, ½ teaspoon kosher salt
Once the milk has begun to simmer, remove from the heat. Slowly stream half of the heated milk into the egg yolk mixture while whisking constantly to avoid curdling the yolks.
Once half of the milk is whisked in and smooth, stream the mixture back into the saucepan with the remaining milk, again, whisking well.
Place the pan back over medium heat, whisking constantly. As soon as the mixture starts to thicken and there is a resistance when whisking, remove the pan from the heat immediately. Continue whisking as the mixture will continue thickening.
Add the vanilla bean paste and butter and whisk to combine.
1½ tablespoons vanilla bean paste, 1½ tablespoons unsalted butter
Use the handle of a wooden spoon or a skewer to poke holes into the top of the cooled cake.
Pour the pastry cream over the surface of the cake and spread to all of the edges. Gently press the pastry cream down onto the cake so that it goes down into the holes that have been poked into the cake.
Cover the cake with plastic wrap so that the plastic wrap is down on the pastry cream. This will help to prevent a skin from forming. Place the pan into the refrigerator to chill for at least 4 hours.