Let the pie crust sit at room temperature for 15 to 20 minutes before starting. To partially blind bake the crust, transfer it to a 9-inch pie pan (save the parchment!) Gently press it into the pan, into the corners and up the sides. Fold the edges underneath themselves to form a thick rim that hangs just over the edge of the pie pan, and crimp it attractively. Prick the crust in several places with a fork. Place the crust into the freezer and chill for 30 minutes to one hour (you can also do this and leave it overnight, if you want to get this step done ahead of time).
Before you take the pie out, preheat the oven to 375°F. Line the inside of the crust with the parchment paper the dough was originally rolled with, then fill it with uncooked rice or dried beans. Bake the crust for 20 minutes, then carefully remove the parchment with the grains or beans inside. Return the crust to the oven and bake for another 16 minutes or so, until the crust is fairly firm and just turning golden brown. Remove and let cool completely on a wire rack, leaving the oven on.
While the crust is baking, make the filling: In a large bowl, whisk together the cornstarch, salt, egg yolks and 1/2 cup of the milk until the cornstarch is dissolved. Whisk in the remaining 2 1/2 cups milk.
In a saucepan melt 3 tablespoons of the butter in a saucepan over medium-low heat, and then add the sugar and stir until the mixture is smooth and bubbly (it will be thick); make sure it doesn't burn. Give the milk mixture a good whisk again, then very slowly pour it into the pot, whisking all the while, until smooth and incorporated. Turn the heat up to medium whisking almost continuously, and let the mixture come to a simmer, then continue whisking until the mixture is thick and smooth, about 3 more minutes. Remove from the heat and stir in the remaining tablespoon butter and the vanilla.
Let the mixture cool for about 10 minutes, stirring occasionally to prevent a skin from forming, then pour it into the mostly baked pie shell. Bake for 15 minutes (it will still be jiggly when you take it out of the oven), then remove and cool completely on a wire rack.
You can serve the pie after it finishes cooling, or to firm it up even more, you can refrigerate it for 2 to 24 hours, which makes it slice more cleanly. Pile on the whipped cream over the top of the pie, swirling it attractively and mounding it so that it covers the filling. Cut into wedges with a clean sharp knife, and drizzle with chocolate sauce if desired.