Prepare a bowl ready for cooling the pastry cream with a fine-mesh sieve
resting in the rim.
Pour the milk into a heavy saucepan. Split the vanilla bean half lengthwise and use the tip of a sharp knife to scrape the seeds into the milk
. Add the salt, then put the pan over medium-high heat until the mixture comes just under a boil. Stir occasionally, making sure that the milk solids are not sticking to the bottom of the pan.
In a mixing bowl, whisk
together the cornstarch and sugar. Add the eggs and whisk until smooth.
When the milk is hot, slowly ladle about 1/3 of the hot milk into the egg mixture, whisking constantly. Pour the egg-milk mixture back into the hot milk. Continue whisking over medium heat until the custard
is as thick as lightly whipped cream
, about 2 minutes. The mixture must come just to the boiling point, only a few slow bubbles.
Remove the pan from the heat and immediately pour the mixture through the sieve into the bowl. Let cool for 10 minutes, stirring occasionally, to release the heat and prevent a skin from forming on top.
Cut the butter into 1-tablespoon pieces. When the pastry cream is ready, add the butter, 1 tablespoon at a time, whisking until smooth before adding the next tablespoon.
To cool the cream: Cover the bowl with plastic wrap, pressing the wrap directly onto the top of the cream. Store in refrigerator until ready to use. Pastry cream will keep, well covered, in the refrigerator for up to 5 days.