In a medium pot over medium heat, combine the milk and cream. Heat until steaming and just below a boil.
In a large mixing bowl, whisk together the sugar, cornstarch, cocoa powder, and salt until fully combined.
Add the egg and whisk lightly to break it up. The dries will not all be mixed together with the egg yet at this stage.
Very slowly pour the hot milk and cream into the bowl while whisking constantly and vigorously to temper the egg and prevent curdling. When all of the liquid has been added, pour the entire mixture back into the saucepan.
Place the saucepan over low heat and whisk continuously until the pudding thickens and begins to bubble.
Once the mixture begins to boil, continue whisking vigorously for 30 to 60 seconds to fully activate the cornstarch.
Remove from heat and immediately strain the pudding through a fine-mesh sieve into a clean mixing bowl to remove any lumps or bits of cooked egg.
Add the chopped chocolate and butter to the hot pudding. Whisk until both have melted and the mixture is smooth and glossy.
Pour the warm pudding into your prepared, fully baked pie shell, spreading it evenly.
Press a piece of plastic wrap directly against the surface of the pudding to prevent a skin from forming.
Refrigerate for at least 3 hours, or until the filling is fully set and completely cool before topping with whipped cream.