Combine the sugar, eggs, and yolk in a medium mixing bowl and whisk until thickened, pale, and foamy — about 3 minutes.
Sift the cornstarch through a fine-mesh sieve into the egg mixture then whisk to combine. Set the bowl on a wet towel (to prevent scooting) and set near the cooktop. Position the sieve over a second mixing bowl and set aside.
Combine the milk and salt in a 3-quart saucepan or saucier and bring to a bare simmer over medium heat — 3 to 5 minutes. Once hot, drizzle about a third of the milk into the sugar and egg mixture, all the while continuously whisking the eggs. Then reverse course and —still whisking — pour the now-warmed egg mixture back into the pot with the milk. Congratulations, you just tempered.
Move the pan back over medium heat and whisk spiritedly. As the mixture just begins to resist the whisk, drop the heat to low and keep whisking until the mixture turns thick and just begins to bubble. This thickening process should take between 1 and 3 minutes.
When the mixture just starts to bubble, you’ll know it’s as thick as it’s going to get, so quickly remove the pan from the heat and pour the mixture through the sieve into the empty bowl, helping it through with a rubber spatula. There will be some odd little scrambled eggs bits in the sieve and that’s what you want to exclude.
Whisk the butter into the strained mixture a piece at a time, making sure each piece melts before introducing the next. Whisk in the vanilla. Cover the pastry cream with plastic wrap, making sure to get the wrap right down on the surface, thus preventing a skin from forming. Although the cream can be used hot, I prefer to pipe it when it’s down to room temperature.
The pastry cream can be refrigerated for up to a week as long as it is tightly sealed.