In a medium bowl, whisk the yolk, egg, sugar (if using), and cornstarch together. Set aside convenient to the stove.

Put the vanilla extract in another medium bowl and place a fine mesh strainer over the top. Set aside convenient to the stove.

In a heavy-bottomed saucepan, heat the water and butter together over medium heat until the butter is melted. The addition of water will help the sugar (added in the next step) to completely dissolve before starting to caramelize.

Add the dark brown sugar and salt, and cook together over medium heat, stirring constantly with a wooden spoon or high-heat spatula. The mixture will look very creamy and bubbly, and then all of a sudden, the butter will separate out and the whole thing will look kind of sad and like a failure. Keep going. In another couple of minutes, the mixture will come back together again. Don't stop stirring. Another way to tell when your butterscotch is done is when you begin to smell caramelized sugar. As it cooks, the mixture will not smell like much of anything. Then it will start to smell a bit nutty from the browned butter, and finally the sugar will begin to caramelize. You will be able to smell it, and that's when it's done. Over medium heat, this may take 10-15 minutes, depending. If you have an instant-read thermometer, check the temp periodically. The butterscotch will be done at around 330F.

Once you actually have butterscotch, pour in about half the milk, and remove the pan from the heat. Do it carefully. The butterscotch will hiss and bubble and then turn into a hard mass. Carefully pry the hard mass off the bottom of the pan with your spoon or spatula and then return the pan to medium-low heat. Add the rest of the milk. NOTE: You can heat the milk until steaming but not boiling to minimize seizing.

Stir until all the butterscotch has melted back into the milk. This could take 4-5 minutes. Just be patient and stir and stir. You will most likely have butterscotch stuck to your spoon or spatula. That's okay. It will melt too. Just keep stirring.

Once the "butterscotch milk" is nice and smooth, continue to heat until the milk is steaming. Then, temper about half the butterscotch into the egg yolk mixture, whisking very well.

Pour the tempered yolks back into the pan and bring to a boil, stirring constantly. Allow the mixture to boil for 2 full minutes, whisking constantly..

Pour the pudding through the fine mesh strainer into the bowl with the vanilla. The mixture will be very thick, so use the pack of your spatula to press it through.

Stir until the vanilla is mixed in.

At this point, you can pour into small bowls or leave it in the large bowl and press plastic wrap down onto the surface of the pudding. Either way, refrigerate until cold, or you can eat it warm. I won't judge you.

See NOTES below for how to serve. Enjoy!