Set aside a bowl to cool the pastry cream with a fine-mesh sieve on top
In another bowl, whisk together the cornstarch and sugar. Add the eggs and whisk until smooth. Set aside the mixture
In a saucepan, pour in the milk and the vanilla bean paste. Add the salt and mix. Place the mixture on medium-high heat until just under a boil. Be sure to stir the mixture occasionally to ensure the milk solids do not stick to the bottom of the pan
When the milk is warmed, add 1/3 of the hot milk into the egg mixture, whisking constantly to ensure the eggs do not cook. After it is combined, pour the egg-milk mixture back into the remaining ⅔ of the hot milk. Whisk over medium heat until the mixture is as thick as lightly whipped cream. It should just come just barely to a boil - be sure not to let it get beyond this as the cream will curdle. Remove from the heat and immediately pour through the sieve into the bowl. Do not leave the pastry cream in the bowl as it will continue to cook.
Let the cream cool for 10 minutes, stirring occasionally. When the pastry cream reaches 140 degrees F, mix in the butter one piece at a time. Stir until smooth before adding the next piece of butter
Cool the pastry cream by tightly covering a bowl with plastic wrap. The plastic should press onto the pastry cream to keep it from developing a skin. After wrapping, place in the refrigerator to chill. Do not whisk the cream once it is chilled as it will break down the cream.