Take three tablespoons of the milk and the cornstarch and mix together in a small bowl to make a slurry.
In a saucepan, mix together the milk, slurry, and salt together.
In a medium bowl, whisk together the sugar and egg.
Take the vanilla bean pod and slice in half. Scrape out the vanilla bean seeds and mix into the egg mixture, then put the empty pod into the milk mixture.
Heat the milk mixture until it starts to simmer and thicken.
Take a cup of the hot milk and slowly drizzle it into the egg mixture as you quickly beat the eggs. Whisk the eggs until it fully incorporates the milk.
Repeat with another cup of the milk.
Add the heavy cream to the saucepan along with the egg mixture.
Stir the pudding until it is thick enough to coat the back of a wooden spoon.
Turn off the heat, then stir in the butter and vanilla extract.
Strain the pudding through a fine mesh strainer. Discard the vanilla bean pod.
Place plastic wrap on your pudding so that it touches the top of your pudding and chill for at least 5 - 6 hours, or until completely chilled through.