Place milk in a medium saucepan on low-medium heat.
Cut the vanilla bean in half lengthwise with a sharp knife. Remove the vanilla beans and place them in the milk. Place the whole vanilla bean in the milk as well.
Let the milk just come to a simmer, not boiling. Turn off the heat source and remove the milk from the heat. Let the vanilla bean infuse flavor for 15 minutes.
In the meantime, separate your eggs. Place the egg yolks in a large heat proof bowl.
Add sugar and cornstarch to the egg yolks and mix together with a whisk.
Remove the vanilla bean from the saucepan. Slowly temper the eggs by adding a couple of tablespoons of the milk to the eggs at a time and vigorously whisking it until fully emulsified.
Continue adding the milk very slowly until fully combined. You do not want to cook the eggs.
Strain the mixture back into the saucepan by placing a sifter or strainer on top of your saucepan. Pour the mixture through the strainer and into the saucepan. Place the saucepan back on the heat source on medium heat.
Whisk the mixture frequently. Heat the mixture until the cornstarch has activated. It should be a few minutes. You will feel the mixture becoming thickened with your whisk (~5 minutes).
Cook for 1 more minute after it has started to thicken.
Remove the vanilla custard from the heat and add the butter. Whisk the butter until it has fully melted into the custard.
Let the custard cool until the pot can go in the fridge. Place a plastic wrap on top of the custard to prevent a film from forming.
Chill the vanilla custard for 2 hours before using, or overnight until you're ready to make your mini mille feuille.