Prepare the Chocolate Pastry:
In a food processor, combine the flour, cocoa powder, powdered sugar, and salt. Pulse until blended.
Add the cold butter and pulse about 7 times until the mixture becomes crumbly.
In a small bowl, whisk the egg, then pour it into the food processor while the motor is running. Continue processing until the dough forms into a cohesive ball.
Scrape the dough onto plastic wrap, shape it into a disk, and wrap tightly. Roll out the dough while wrapped to stretch it slightly.
Refrigerate the dough for 2 hours or overnight.
Preheat your oven to 400ºF (200ºC). Roll out the chilled dough on a lightly floured surface to an 11-inch circle. Transfer it to a 9-inch pie plate and crimp the edges.
Line the pie dough with parchment paper and add pie weights. Bake for 25 minutes. Remove the parchment and weights, then bake for an additional 5 minutes. Set aside to cool.
Lower the oven temperature to 325ºF (160ºC).
Prepare and Bake the Coffee Custard Filling:
In a medium saucepan, heat the milk, cream, brown sugar, espresso powder, and salt over medium heat until small bubbles form along the edges (around 120ºF).
In a separate bowl, whisk the eggs, egg yolks, granulated sugar, and vanilla extract.
Slowly temper the eggs by pouring 1-2 cups of the warmed milk mixture into the eggs while whisking constantly. Then pour the tempered egg mixture back into the saucepan.
Cook the custard over medium heat for 2-3 minutes until it thickens slightly and reaches 160ºF. Check by coating a spoon with the custard and drawing a line with your finger; the line should hold.
Strain the custard through a fine mesh sieve twice to remove any lumps. Let it cool slightly for about 5 minutes.
Pour the warm custard into the pre-baked pie crust, popping any bubbles on the surface.
Bake the pie for 35-40 minutes until the edges are set and the center is slightly wobbly. The pie should reach 180ºF.
Let the pie cool completely on a wire rack, then refrigerate until ready to serve.
Serve cold with whipped cream and a dusting of powdered sugar.