Add brown sugar (1 cup), water (2/3 cup), and salt (1/4 teaspoon) together in a medium heavy-bottom saucepan over medium-low heat. Allow this mixture to cook and bubble, without stirring, until the mixture becomes darker brown, about 5-6 minutes. To be extra careful, I use a candy thermometer to confirm doneness, at 240°F (115ºC).
When the brown sugar mixture reaches 240°F (115ºC), remove from heat and whisk in butter (6 tablespoons). Whisk until even is smooth.
In a small bowl, sift together flour (2 tablespoons) and cornstarch (3 tablespoons).
Add flour mixture to a 3-quart saucepan. Slowly add and whisk in milk (1 cup) and heavy cream (1 cup).
When the mixture is smooth, whisk in the hot brown sugar and butter mixture.
Over medium-low heat, cook, scraping the bottom and sides of the pan constantly with a wooden spoon. If lumps form (it happens, don't worry!), pour the mixture through a fine sieve into a bowl the return the mixture to the pan. Continue to heat and allow to boil for 1 minute. Remove from heat.
Temper the egg yolks by stirring in a couple of tablespoons of the hot mixture into the egg yolks while whisking constantly with a wire whisk. Repeat 2 more times.
Pour the tempered egg yolks into the hot mixture, stirring just until combined.
Continue to cook on low, stirring constantly, and bring the mixture to a low boil. Continue to stir and scrape the pan and simmer for 1 minute.
Remove from heat and stir in vanilla (1 1/2 teaspoons).
Pour into a large bowl. Very gently, constantly fold the mixture to allow steam to evaporate, until the mixture is cool.
Pour into blind baked pie shell and refrigerate for 4 -6 hours.