In a medium saucepan over medium-high heat, bring the milk, cream, 1/4 cup of the sugar, and salt to a simmer, stirring occasionally.
2 cups whole milk, 1 1/2 cups heavy cream, 1/2 cup granulated sugar divided, 1/4 teaspoon salt
While the milk mixture heats, whisk together the remaining sugar, cornstarch, and egg yolks until smooth and creamy.
1/4 cup cornstarch, 9 egg yolks
When the milk mixture is hot, slowly pour 1 cup of the hot liquid into the egg mixture, whisking to temper the egg yolks. Then slowly whisk the tempered yolks back into the saucepan of simmering milk and cream. Reduce the heat to medium and continue to cook, whisking constantly, until the mixture thickens and large bubbles start to burst on top, about 30 seconds.
Remove the pan from the heat and immediately whisk in the cubed butter and chocolate until completely melted and smooth. Stir in the vanilla, then pour into the prepared pie crust. Cover with plastic wrap, pressing into the surface of the filling so a skin doesn't form, and refrigerate for 4 hours until the filling is set and chilled.
8 Tablespoons salted butter, 8 ounces semi-sweet chocolate, 2 ounces bittersweet chocolate, 1 1/2 teaspoons vanilla extract