Have ready a fine-mesh strainer placed over a large heatproof bowl.
In a heavy, medium saucepan over medium heat, combine the milk and cream and heat just until bubbles begin to form. Do not let the mixture come to a boil.
Meanwhile, in a bowl, whisk together the cornstarch, sugar, and cocoa powder until blended.
In a separate bowl, whisk the eggs with the salt until blended. Slowly add them to the sugar mixture and whisk until well combined.
Still whisking constantly, slowly add half of the hot milk mixture to the egg mixture.
Pour the egg mixture back into the pan containing the rest of the milk mixture and cook over medium heat, whisking constantly, until the mixture has visibly thickened and registers 208°F (98°C) on a thermometer, 4 to 7 minutes.
Immediately pour the pudding through the strainer. Add the chocolate to the pudding and let the heat of the mixture melt it.
When the chocolate has melted, blitz with an immersion blender until no lumps are visible, about 5 minutes. Stop the blender and scrape down the sides of the bowl as needed. (Alternatively, you may use a blender and work in small batches, or use a whisk to blend by hand, being extremely careful with the hot mixture.) The pudding will keep, well covered, in the refrigerator for up to 4 days.
Pour the chocolate pudding into the pie shell. Refrigerate until the surface is cold and set, at least 1 1/2 hours.