Bring 2 cups of the milk to a boil in a medium saucepan.
While it is heating, combine sugar, cornstarch, salt and vanilla bean (if you’re replacing it with extract, don’t add it yet; if you’d like to toss the leftover vanilla bean pods in the pot with the simmering milk for an extra vanilla boost, go for it) in the bottom of a medium, heatproof bowl.
Gradually whisk in the remaining 2/3 cup whole milk, a little at a time so lumps do not form, then whisk in the egg.
Once milk is boiling, very gradually add it to the cornstarch mixture in the bowl, whisking the whole time.
Return the mixture back to the saucepan, stirring constantly with a silicon spatula or wooden spoon. Once it comes to a simmer, cook it for one minute longer (which will cook the cornstarch and egg fully). Stir in vanilla extract, if you’re using it and divide pudding among 6 dishes.
Chill in refrigerator until fully set, about 2 hours.[If you don't like pudding skin, just press a piece of plastic wrap against the top of the pudding before you chill it.]