In your saucepan over medium heat, melt the butter. Stir in the packed brown sugar and salt. Let it bubble away for about 2 to 3 minutes, stirring constantly, until it looks like melted lava and smells like toffee. Don't let it burn, but we want it deep gold!
While the sugar bubbles, whisk your cornstarch into 1/4 cup of the cold milk until smooth. Whisk in the egg yolks. Set this aside.
Very slowly, pour the remaining 1 3/4 cups of milk into the hot sugar mixture. The sugar might seize up and get hard, don't panic! Just keep whisking over the heat and it will melt back into the milk.
Now let’s add our vanilla and stir again.
Once the mixture is smooth and hot, take a big spoonful of it and whisk it quickly into your egg/cornstarch bowl (this "tempers" the eggs so they don't scramble).
Then, pour that whole egg mixture back into the saucepan.
Whisk constantly until the pudding thickens and just starts to bubble. Let it boil for exactly 1 minute to cook the starch.
Remove from heat and if you want it extra silky, pour it through a strainer into a bowl.
Divide the warm pudding into your 4 small jars. Press a little piece of plastic wrap directly onto the surface if you want to prevent a "skin" from forming, or leave it off if you’re a fan of the pudding skin!
Refrigerate for at least 2 hours until set.