Blind-bake or fully bake the 9-inch crust and let it cool completely.
Whisk sugar, cocoa powder, cornstarch, and salt together in a saucepan.
Slowly add milk and cook 7–9 minutes until thick with gentle bubbles.
Temper the egg yolks, return them to the pot, and cook 2–3 minutes until silky.
Stir in butter and vanilla off heat until smooth and glossy.
Pour the custard into the crust, cover the surface, and chill at least 4 hours.
Whip the cream with powdered sugar and vanilla, then spread over the pie.