Preheat your oven to 180°C (350°F) and grab a 23 cm (9-inch) pie dish.
Break the cookies into chunks and place them in a food processor, then pulse until they become fine crumbs. Add the melted butter and blend again until the texture looks like damp sand.
Pour the crumb mixture into the pie dish and press it firmly into the base and up the sides using your fingers or the bottom of a glass. Make sure it’s even all around.
Bake the crust for about 10 minutes until slightly puffed, then remove it from the oven. Press the crust gently with a spatula while it’s still warm to compact it, then let it cool completely before adding the filling.
In a large saucepan, whisk together the cornflour, sugar, and salt. Add the milk, cream, and egg yolks, and whisk until smooth.
Place the saucepan over medium-high heat and cook, whisking occasionally at first, then constantly once it starts to steam. Keep whisking until the mixture thickens and slow bubbles appear, which should take about 6 minutes.
Once it thickens, keep whisking for another 45 seconds, then remove from the heat. Add the butter, chopped dark and milk chocolates, and vanilla. Stir until everything is melted and the filling is silky smooth.
Pour the hot chocolate filling into the cooled crust, smoothing the surface with a spatula. Gently lay a piece of parchment paper directly on top of the filling to stop a skin from forming.
Let the pie cool at room temperature for about 2 hours, then transfer it to the fridge and chill for at least 12 hours so the filling can fully set.
When ready to serve, whip the cream, sugar, and vanilla together until soft peaks form, then spread it over the chilled pie.
Sprinkle the top with grated chocolate, slice carefully, and serve straight from the dish.