Bring the half-and-half, half the sugar, and the salt to a simmer in a medium saucepan over medium-high heat, stirring occasionally.
As the half-and-half mixture begins to simmer, in a separate bowl, whisk the egg yolks, the remaining sugar, and cornstarch until smooth.
Slowly whisk about 1 cup simmering half-and-half mixture into the yolks to temper them. (This means to slowly change the temperature so the eggs don’t curdle.) Then slowly whisk the tempered yolks into the remaining simmering half-and-half mixture and reduce the heat to medium. Whisking constantly, return the mixture to a simmer and cook until thickened and a few bubbles burst on the surface, anywhere from 30 seconds to 2 minutes. Remove from the heat and immediately whisk in the butter, then the chocolates, and finally the vanilla, whisking until completely smooth.
Pour the warm filling into the baked, cooled pie crust. Cover with plastic wrap, pressing it flush against the surface of the filling to prevent a skin from forming. Refrigerate until the filling is cold and firm, at least 3 hours. (The pie, without the topping, can be wrapped tightly and refrigerated for up to 1 day.)