Place chocolate in small bowl. In heavy saucepan over medium-high heat, whisk together cream and 1 tbsp. butter until the mixture begins to bubble around the edges. Pour hot mixture into chocolate bowl and whisk until smooth. Set aside.
Combine sugar, cornstarch, and salt in a pot. Slowly whisk in milk over medium-high heat. Whisk until thick and bubbling, 6 to 8 minutes. Whisking constantly, slowly pour the warm milk mixture into the yolks. Return mixture to pot and cook over medium heat, stirring constantly, until it returns to a boil, 1 to 2 minutes. Remove from heat immediately and strain into a bowl; stir in remaining 2 tbsp. butter and vanilla.
Let vanilla cream cool 15 minutes (until room temperature). Pour chocolate sauce into cooled piecrust and let sit for 30 minutes. Pour vanilla custard over the chocolate and smooth surface with a spatula. Let pie cool to room temperature, then cover with plastic wrap and refrigerate until firm, at least 3 hours or overnight.