Place chocolate in a large bowl. In heavy-bottomed saucepan over medium-high heat, whisk together milk and 1/4 cup sugar until mixture begins to bubble around edges.
In separate large bowl, whisk together yolks, 1/4 cup sugar, cornstarch, and salt. Whisking the yolks constantly, slowly pour in the hot milk mixture.
Return mixture to the pot and cook over medium heat, stirring constantly, until it thickens, about 3 minutes. (Do not let mixture come to a boil or it will curdle). Remove from heat immediately and strain into the bowl of chocolate. Whisk until smooth. Stir in vanilla.
Let chocolate custard filling cool 15 minutes. Pour custard into crust and smooth surface with spatula. Let pie cool to room temperature, then cover with plastic wrap and refrigerate overnight. Top with whipped cream before serving.