In a medium saucepan with a heavy bottom, whisk together the sugar, cornstarch, and kosher salt.
Whisk in the eggs until smooth and homogeneous. There should be no streaks of eggs and no lumps of cornstarch. Once the mixture is fully incorporated, add the milk, vanilla seeds, and scraped pod, and whisk.
Before turning the heat on, measure your butter and vanilla extract. Stirred custards wait for no one.
Cook and cool the pudding:
Cook over medium heat, whisking constantly, until bubbly and thickened. Once the pudding has started to bubble, you will need to whisk for at least 1 minute to thicken it and cook away the cornstarch flavor. Improperly cooked cornstarch also has an unpleasant mouthfeel.
Remove the pot from the burner and stir in the butter and vanilla extract. Whisk until there are no streaks of butter. We add the vanilla extract at the end because cooking vanilla extract will actually dilute the flavor.
Pour the pudding into a bowl, plastic-lined sheet tray, or individual cups. Cover with plastic wrap touching the surface of the pudding to prevent a skin. Then, poke a few holes to allow the steam to escape. Refrigerate until set.
For the pudding pictured in the photos I cooled the pudding on a sheet tray as pictured above, whisked it once cool and then spooned it into the cups. You can also use a piping bag to keep the sides perfectly clean. Okay, you caught me. That’s totally what I did!