In a medium saucepan, whisk together the sugar, cornstarch, and kosher salt. Be sure to whisk all the clumps out of the cornstarch.
Whisk in eggs until smooth and homogenous. There should be no streaks of eggs and no lumps of cornstarch. Once fully incorporated, slowly whisk the milk into the egg mixture.
Have your caramel sauce scaled and ready before turning the heat on.
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 your pudding and cook away the cornstarch flavor.
Remove the pan from the burner and stir in your caramel sauce. Whisk until completely combined.
Pour the pudding into a bowl, plastic lined sheet tray, or individual cups. Cover with a piece of plastic wrap touching the surface of the pudding to prevent a skin from forming. Then, poke a few holes to allow the steam to escape. Refrigerate until set.
